Flat Currents of Green Schwarz Superstring in AdS 2 S 2 Background
|
|
- Poppy Taylor
- 6 years ago
- Views:
Transcription
1 Commun. Theor. Phys. (Beijing, China) 45 (2006) pp c International Academic Publishers Vol. 45, No. 4, April 15, 2006 Flat Currents of Green Schwarz Superstring in AdS 2 S 2 Background WANG Xiao-Hui, WANG Zhan-Yun, CAI Xiao-Lin, SONG Pei, HOU Bo-Yu, and SHI Kang-Jie Institute of Modern Physics, Northwest University, Xi an , China (Received August 25, 2005) Abstract From the κ symmetric action of IIB string in AdS 2 S 2 background given by Zhou, we derive the equations of motion. By using the twisted dual transformation which was introduced by Hou, we construct the flat currents, conserving non-local charge with one free parameter, for the superstring in AdS 2 S 2. PACS numbers: Hf Key words: Green Schwarz superstring, integrability, AdS 2 S 2 1 Introduction Recently, motivated by the AdS/CFT correspondence, [1 3] there has been much interest in the role of integrability in the world-sheet theory of type IIB strings in AdS 5 S 5. In Ref. [4], Bena, Polchinski, and Roiban constructed a hierarchy of infinite nonlocal conserved charges for the Green Schwarz superstring in AdS 5 S 5 spacetime, implying that the world-sheet sigma model is completely integrable. Subsequently Vallilo showed [5] that such charges also exist in the pure-spinor formalism for the superstring. These charges are the analogues of the nonlocal charges which have long been known to exist in the sigma models on symmetric spaces, [6 8] and their discovery allows integrable field theory to be applied to the world-sheet theory of superstrings in AdS 5 S 5. [9,10] In the pure-spinor formalism it has been argued that the charges survive quantum-mechanically. [11,12] It is important to study the AdS/CFT correspondence in the cases with lower-dimensional space, since as a toy model, it is easier to handle for better understanding the correspondence. In an important work [13] Metsaev and Tseytlin (MT) have provided a method to construct the Green Schwarz (GS) superstring action in AdS 5 S 5 background, then Bena, Polchinski, and Roiban [4] gave a method to construct the flat currents of this model in the coset base. Soon after Hou et al. [14,15] used another way to construct the flat currents in the original group base. In fact those two methods are equivalent. Recently Bin Chen et al. have studied the AdS 3 S 3 string in Ref. [16]. In this paper we focus on the AdS 2 S 2 string. Our main aim is to construct explicitly a one-parameter family of flat currents which would lead to classical nonlocal charges. The type IIB GS superstring action is constructed in AdS 2 S 2 background in terms of supercoset formalism, which was introduced by Zhou. [17] This action possesses global PSU(1, 1 2) super-invariance, has κ-symmetry and 2D reparametrization invariance as its local symmetries, and reduces to the conventional type IIB GS superstring action in the flat background limit. For comparison with the original work of MT, we change the basis of the algebra psu(1, 1 2), and give the Maurer Cartan equations, then rewrite the GS superstring action via supercoset method, and derive the equations of motion. The action and the equations of motion have the same form as the ones in the AdS 5 S 5 string, [13] but the charge conjugation matrix C and C are both symmetric. Instead of the method given in Ref. [4], we use the dual twisted transformation which was introduced by Hou and construct a family of flat currents which would naturally lead to a hierarchy of classical conserved nonlocal charges. With the help of the world-sheet Hodge dual of the equations of motion, we show that these new currents are really flat. This paper is organized as follows. We first review the AdS 2 S 2 string. In Sec. 2 we give the Lie algebra of the superalgebra psu(1, 1 2) in a new base, then we define the Maurer Cartan 1-forms with respect to these generators and write down the Maurer Cartan equations. In Sec. 3 we rewrite the action of AdS 2 S 2 string using the Maurer Cartan 1-forms of the new base and then derive the equations of motion. Then in Sec. 4 we explicitly construct a one-parameter family of the flat currents in AdS 2 S 2 superstring. At last, we summarize our results with discussion in Sec psu(1, 1 2) Superalgebra We begin with the psu(1, 1 2) superalgebra. The target space of string theory in AdS 2 S 2 with 8 supersymmetry generators is the supercoset manifold PSU(1, 1 2) SO(1, 1) SO(2), The project supported by National Natural Science Foundation of China under Grant No xhwang@nwu.edu.cn
2 664 WANG Xiao-Hui, WANG Zhan-Yun, CAI Xiao-Lin, SONG Pei, HOU Bo-Yu, and SHI Kang-Jie Vol. 45 whose bosonic part is SO(1, 2) SO(3) SO(1, 1) SO(2) = AdS 2 S 2. The bosonic generators of this supergroup are the monenta and Lorentz transformation on AdS 2 and S 2, P a, J ab and P a, J a b, and the fermionic generators are the two D = 4 Majorana Weyl spinors Q αα I (α, α = 1, 2; I = 1, 2). In what follows we use the same notations as that in Ref. [13]. The ordinary Latin letters a, b = 0, 1 are the SO(1,1) vector indices (AdS 2 tangent space). The primed Latin letters a, b = 2, 3 are the SO(2) vector indices. The ordinary Greek letters α, β = 1, 2 are the SO(1,1) spinor indices. The primed Greek letters α, β = 1, 2 are the SO(2) spinor indices. We also use the 2 2 matrices ɛ IJ = ɛ JI, ɛ 12 = 1, and S IJ diag (1, 1) to contract the indices I = 1, 2. The 4-dimensional Dirac matrices Γâ and the corresponding charge conjugation matrix C can be represented as Γ a = γ a I, Γ a = I γ a, C = C C, (1) where I is the 2 2 unit matrix. The generators of the SO(1,1) and SO(2) Clifford algebras are 2 2 matrices γ a and γ a, ( ) ( ) i γ 0 =, γ 1 i =, (2) i i ( ) ( ) γ 2 1 i =, γ 3 =, (3) 1 i and the charge conjugation matrices are ( ) C = C 1 =. (4) 1 Then the conjugate supercharge Q αα I is defined by Q I = (Q I ) t CC. (5) Thus psu(1, 1 2) superalgebra is given by [P a, P b ] = J ab, (6) [P a, P b ] = J a b, (7) [J ab, J cd ] = [J a b, J c d ] = 0, (8) [P a, J bc ] = η ab P c η ac P b, (9) [P a, J b c ] = η a b P c η a c P b, (10) [Q I, P a ] = i 2 ɛ IJQ J γ a, (11) [Q I, P a ] = 1 2 ɛ IJQ J γ a, (12) [Q I, J ab ] = 1 2 Q Iγ ab, (13) [Q I, J a b ] = 1 2 Q Iγ a b, (14) {Q αα I, Q ββ J} = δ IJ [ 2i C α β (Cγa ) αβ P a + 2C αβ (C γ a ) α β P a ] + ɛ IJ [C α β (Cγab ) αβ J ab The left-invariant Cartan 1-forms are given by C αβ (C γ a b ) α β J a b ]. (15) L A = dx M L A M, X M = (x, θ) (16) G 1 dg = L A T A L a P a + L a P a Lab J ab La b J a b + Lαα I Q αα I, (17) where G = G(x, θ) is a coset representative in PSU(1, 1 2). The Maurer Cartan 1-form satisfies the zero-curvature equation d(g 1 dg) = G 1 dg G 1 dg. Then decompose it according to the generators of the Lie algebra, we get the following Maurer Cartan equations: dl a = L b L ba i L I γ a L I, (18) dl a = L b L b a + L I γ a L I, (19) dl ab = L a L b + ɛ IJ LI γ ab L J, (20) dl a b = L a L b ɛ IJ LI γ a b L J, (21) dl I = i 2 γ aɛ IJ L J L a γ a ɛ IJL J L a γ abl I L ab γ a b LI L a b. (22) In this paper we set L αα I Q ββ J = Q ββ JL αα I, which is the same as in Ref. [13] but different from the convention in Ref. [17]. In Eqs. (18) (21) we set ( L I ) αα = L µµ I C µα C µ α = (LI CC ) αα according to Eq. (5). 3 κ Symmetric Action and Equations of Motion The AdS 2 S 2 GS superstring action is given as superspace sigma model, [13] PSU(1, 1 2) SO(1, 1) SO(2) S = S 0 + S 1, (23) S 0 = 1 d 2 σ gg ij (L a i L a j + L a i L a j ), (24) 2 M 3 S 1 = i L W Z (25) M 3 = i S IJ (L a L I γ a L J + il a L I γ a L J ). (26) M 3 Here g = det g ij, g ij g jk = δ ik, i, j = 0, 1 and g ij is the metric of the world-sheet. This action is invariant with respect to the local κ-transformations in terms of δx a δx M L a M, δx a δx M L a M, δθ I δx M L I M,
3 No. 4 Flat Currents of Green Schwarz Superstring in AdS 2 S 2 Background 665 i.e. G 1 δg δx a P a + δx a P a δxab J ab δxa b J a b + δθαα I Q αα I, δ κ x a = 0, δ κ x a = 0, (27) δ κ θ I = 2(L a i γ a il a i γ a )κ ii, (28) δ κ ( gg ij ) = 16i g(p jk L 1 kκ i1 + P jk + L 2 kκ i2 ). (29) Here P ij ± (1/2)(g ij ±(1/ g)ɛ ij ) are the projection operators, and 4-component spinor κ ii satisfy the (anti-) selfduality constraints, P ij κ 1 j = κ i1, P ij + κ 2 j = κ i2, (30) which can be written as (1/ g)ɛ ij κ 1 j = κ i1, (1/ g) ɛ ij κ 2 j = κi2, i.e. (1/ g)ɛ ij κ I j = SIJ κ ij. To derive the EOM and also to check the κ invariance, we decompose the following equation, δ(g 1 dg) = [G 1 dg, G 1 δg ] + d(g 1 δg) (31) according to the generators of the Lie algebra and obtain the variations of the Cartan 1-forms: δl a = dδx a + L ab δx b + L b δx ba + 2 i L I γ a δθ I, (32) δl a = dδx a + L a b δx b + L b δx b a 2 L I γ a δθ I, (33) δl I = dδθ I + i 2 ɛ IJ(δx a γ a + iδx a γ a )L J i 2 ɛ IJ(L a γ a + il a γ a )δθ J 1 4 (δxab γ ab + δx a b γ a b )L I (Lab γ ab + L a b γ a b )δθ I. (34) The WZ term L WZ in Eq. (25) is also a closed 3-form and its variation is given by δl WZ = dλ, Λ = S IJ ( L I γ a L J δx a + i L I γ a L J δx a + 2L a L I γ a δθ J + 2iL a L I γ a δθ J ). (36) From the variation of action (23), the equations of motion are obtained, The variation of the metric g ij gives the Virasoro constraint, i ( gg ij L a j ) + gg ij L ab i L b j + iɛ ij S IJ LI i γ a L J j = 0, (37) i ( gg ij L a j ) + gg ij L a b i L b j ɛ ij S IJ LI i γ a L J j = 0, (38) (γ a L a i + iγ a L a i )( gg ij δ IJ ɛ ij S IJ )L J j = 0. (39) (35) L a i L a j + L a i L a j = 1 2 g ijg kl (L a kl a l + L a k L a l ). (40) From the variation of action one can check that the κ symmetry is manifest. 4 Flat Currents of AdS 2 S 2 String 4.1 Hodge Dual of Cartan Forms L a and L a To construct a one-parameter family of nonlocal currents from the κ-symmetric actions of Green Schwarz superstring in AdS 2 S 2 background, we firstly introduce the world-sheet Hodge dual of the Maurer Cartan 1-forms L a and L a. Let that is gg ij L a i ɛ jk L a k, (41) gg i1 L a i ɛ 12 L a 2 = L a 2, (42) gg i2 L a i ɛ 21 L a 1 = L a 1. (43) Thus the EOM (37) becomes ɛ jk j L a k + L ab j ɛ jk L b k + is IJ ɛ jk LI j γ a L J k = 0. (44) Then multiplying by dσ j dσ k on both sides of the above equation, we get d L a + L ab L b + is IJ LI γ a L J = 0. (45) In a similar way the EOM (38) and (39) become d L a + L a b L b S IJ LI γ a L J = 0, (46) δ IJ ( L a γ a + i L a γ a ) L J + S IJ (L a γ a + il a γ a ) L J = 0. (47) The above three equations, which are very useful to constructing the flat currents, are the EOM in terms of the Hodge dual of the Maurer Cartan 1-forms L a and L a. [14]
4 666 WANG Xiao-Hui, WANG Zhan-Yun, CAI Xiao-Lin, SONG Pei, HOU Bo-Yu, and SHI Kang-Jie Vol Twisted Dual Transformations Let us now introduce the twisted dual transformations [14,15,18] on psu(1, 1 2) superalgebra, L a (λ) = 1 2 (λ2 + λ 2 )L a (λ2 λ 2 ) L a, (48) L a (λ) = 1 2 (λ2 + λ 2 )L a (λ2 λ 2 ) L a, (49) L ab (λ) = L ab, L a b (λ) = L a b, (50) L 1 (λ) = λl 1, L 2 (λ) = λ 1 L 2. (51) 4.3 Construction of Flat Currents Using the above dual twisted transformation, we have obtained the new Cartan 1-forms L(λ), which we use to construct the flat currents. The most important thing left to do is to check whether these Cartan 1-forms L(λ) satisfy the Maurer Cartan equations (18) (22). Now we check the new Maurer Cartan equations one by one. With the help of MC equation (18), the dual twisted transformation equations (48) (51) and Eq. (45), we get Next, for the MC equation (20) dl a (λ) = 1 2 (λ2 + λ 2 )dl a (λ2 λ 2 )d L a ( 1 = 2 (λ2 + λ 2 )L b (λ2 λ 2 ) L b) L ba iλ 2 L1 γ a L 1 iλ 2 L2 γ a L 2 = L b (λ) L ba (λ) i L I (λ)γ a L I (λ). dl ab (λ) = dl ab = L a L b + ɛ IJ LI γ ab L J (52) = L a (λ) L b (λ) + ɛ IJ LI (λ)γ ab L J (λ). (53) Here the second term (ɛ IJ LI γ ab L J = ɛ IJ LI γ ab L J ) is obvious whereas the first term is not straightforward. To identify L a L b = L a (λ) L b (λ), (54) we have used the following properties of Cartan 1-forms: In a similar way we can check the MC equations (19) and (21) A B = A B, (55) A B = A B. (56) dl a (λ) = L b (λ) L b a (λ) + L I (λ)γ a L I (λ), (57) dl a b (λ) = L a (λ) L b (λ) ɛ IJ LI (λ)γ a b L J (λ). (58) Then there remains the MC equation (22) to check. Since the fermionic Cartan 1-forms L 1 and L 2 have different transformation rules, the best way is to write down them separately. The Hodge dual of the third equation of motion is also useful, so we write Eq. (47) more explicitly, To check the MC equation (22) we first consider the term (L a γ a + il a γ a + L a γ a + i L a γ a ) L 1 = 0, (J = 1), (59) (L a γ a + il a γ a L a γ a i L a γ a ) L 2 = 0, (J = 2). (60) i 2 γ aɛ IJ L J (λ) L a (λ) γ a ɛ IJL J (λ) L a (λ) [( λ 2 = i 2 ɛ IJ 2 ( λ ) (L a γ a + il a γ a + L a γ a + i L a γ a ) L J (λ) ) (L a γ a + il a γ a L a γ a i L a γ a ) L J (λ) ]. (61) Substituting Eqs. (59) and (60) into the above equation, we obtain { i 2 γ aɛ IJ L J (λ) L a (λ) + 1 i 2 γ a ɛ IJL J (λ) L a 2 (λ) = λ(la γ a + il a γ a ) L 2, (I = 1), i 2 λ 1 (L a γ a + il a γ a ) L 1, (I = 2). Therefore we get dl 1 (λ) = λdl 1 (62)
5 No. 4 Flat Currents of Green Schwarz Superstring in AdS 2 S 2 Background 667 = λ i 2 (La γ a + il a γ a ) L 2 + λ 1 4 γ abl 1 L ab + λ 1 4 γ a b L1 L a b = i 2 γ al 2 (λ) L a (λ) γ a L2 (λ) L a (λ) γ abl 1 (λ) L ab (λ) γ a b L1 (λ) L a b (λ), (63) dl 2 (λ) = i 2 γ al 1 (λ) L a (λ) 1 2 γ a L1 (λ) L a (λ) γ abl 2 (λ) L ab (λ) γ a b L2 (λ) L a b (λ). (64) In general dl I (λ) = i 2 γ aɛ IJ L J (λ) L a (λ) γ a ɛ IJL J (λ) L a (λ) γ abl I (λ) L ab (λ) γ a b LI (λ) L a b (λ). (65) In conclusion, we have checked that all these new Cartan 1-forms L(λ) satisfy the Maurer Cartan equations. Thus the current defined as satisfies J (λ) L a (λ)p a + L a (λ)p a Lab (λ)j ab La b (λ)j a b + Lαα I (λ)q αα I (66) dj (λ) + J (λ) J (λ) = 0, (67) and J (λ) is a flat current with parameter λ. Existence of the λ-dependent flat connections easily leads to the infinite number of conserved quantities. Thus the equation T (λ) 1 dt (λ) = J (λ) (68) is integrable. This leads to the integral round a contour as shown in Fig. 1. P exp = P exp b a t2 t 1 Fig. 1 Integral round a contour. t2 J σ (λ, t 1, σ)dσ P exp J τ (λ, τ, b)dτ t 1 J τ (λ, τ, a)dτ P exp b a J σ (λ, t 2, σ)dσ. (69) For periodic case (J (λ, τ, a) = J (λ, τ, b)), we see that Tr (P exp b a J σ(λ, t, σ)dσ) is independent of t, where the trace is taken in the group PSU(1, 1 2). For infinity boundary, when J (λ, τ, σ = ± ) 0, The monodromy T (λ, t) = P exp J σ (λ, t, σ)dσ is also independent of t. In both cases, we have conserved quantities with one parameter λ, suggesting that the system is integrable. 5 Conclusion and Discussion In this paper we construct a one-parameter family of nonlocal currents from the κ-symmetric action of Green Schwarz superstring in AdS 2 S 2 background. This oneparameter family of flat currents would naturally lead to a hierarchy of classical conserved nonlocal charges by the standard method. This fact is a characteristic property that the second sigma model of AdS 2 S 2 is completely integrable at least at the classical level. The charges are constructed by first identifying a family of currents J (λ), depending smoothly on a spectral parameter λ that are valued in some Lie-algebra psu(1, 1 2) and that are flat: dj (λ) + J (λ) J (λ) = 0. One then constructs the monodromy matrix T (λ) (t) = P exp (+,t) (,t) J (λ), which is conserved by virtue of the flatness of J(λ), and the non-local charges are obtained by expanding T (λ) in powers of the spectral parameter. For the periodic boundary condition (closed string) we have ( ) Tr T (λ) (t) = Tr P exp J σ (λ, t, σ)dσ, is also a conserved quantity. In principle with these formulae one can start the heavy machinery of the inverse scattering method. But even in the bosonic case this is not straightforward because of the possible quantum anomalies. We will not proceed with it here and only notice that this hidden symmetry must manifest itself in the spectrum of the anomalous dimensions. The correspondence and the possible role
6 668 WANG Xiao-Hui, WANG Zhan-Yun, CAI Xiao-Lin, SONG Pei, HOU Bo-Yu, and SHI Kang-Jie Vol. 45 played by the integrable structure deserve further investigation. It is said that the existence of the Z 4 grading in the superalgebras plays a key role in the construction of flat currents [4,19] and the κ symmetry is also an important ingredient in the study of integrability of AdS string. [16] However, the role of κ symmetry and relations between κ symmetry and the integrable structure need further study. References [1] J.M. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231, [arxiv:hep-th/ ]. [2] S.S. Gubser, I.R. Klebanov, and A.M. Polyakov, Phys. Lett. B 428 (1998) 105, [arxiv:hep-th/ ]. [3] E. Witten, Adv. Theor. Math. Phys. 2 (1998) 253, [arxiv:hep-th/ ]. [4] I. Bena, J. Polchinski, and R. Roiban, Phys. Rev. D 69 (2004) , [arxiv:hep-th/ ]. [5] B.C. Vallilo, JHEP 0403 (2004) 037, [arxiv:hepth/ ]. [6] H. Eichenherr and M. Forger, Commun. Math. Phys. 82 (1981) 227. [7] J.H. Schwarz, Nucl. Phys. B 447 (1995) 137, [arxiv:hepth/ ]. [8] G. Mandal, N.V. Suryanarayana, and S.R. Wadia, Phys. Lett. B 543 (2002) 81, [arxiv:hep-th/ ]. [9] M. Hatsuda and K. Yoshida, [arxiv:hep-th/ ]. [10] A. Das, J. Maharana, A. Melikyan, and M. Sato, JHEP 0412 (2004) 055, [arxiv:hep-th/ ]. [11] N. Berkovits, JHEP 0502 (2005) 060, [arxiv:hepth/ ]. [12] N. Berkovits, JHEP 0503 (2005) 041, [arxiv:hepth/ ]. [13] R.R. Metsaev and A.A. Tseytlin, Nucl. Phys. B 533 (1998) 109, [arxiv:hep-th/ ]. [14] Bo-Yu Hou, Dan-Tao Peng, Chuan-Hua Xiong, and Rui- Hong Yue, [arxiv:hep-th/ ]. [15] Chuan-Hua Xiong, Acta Phys. Sin. 54 (2005) 0047 (in Chinese). [16] Bin Chen, Ya-Li He, Peng Zhang, and Xing-Chang Song, Phys. Rev. D 71 (2005) , [arxiv:hep-th/ ]. [17] Jian-Ge Zhou, Nucl. Phys. B 559 (1999) 92, [arxiv:hepth/ ]. [18] A.M. Polyakov, Mod. Phys. Lett. A 19 (2004) 1649, [arxiv:hep-th/ ]. [19] C.A.S. Young, [arxiv:hep-th/ ].
The Affine Hidden Symmetry and Integrability of Type IIB Superstring in AdS 5 S 5
The Affine Hidden Symmetry and Integrability of Type IIB Superstring in AdS 5 S 5 arxiv:hep-th/0406239v1 25 Jun 2004 Bo-Yu Hou a, Dan-Tao Peng ab, Chuan-Hua Xiong a, Rui-Hong Yue a a Institute of Modern
More informationTopological DBI actions and nonlinear instantons
8 November 00 Physics Letters B 50 00) 70 7 www.elsevier.com/locate/npe Topological DBI actions and nonlinear instantons A. Imaanpur Department of Physics, School of Sciences, Tarbiat Modares University,
More informationMaster Symmetry and Wilson Loops in AdS/CFT
Master Symmetry and Wilson Loops in AdS/CFT Florian Loebbert Humboldt University Berlin Phys.Rev. D94 (2016), arxiv: 1606.04104 Nucl.Phys. B916 (2017), arxiv: 1610.01161 with Thomas Klose and Hagen Münkler
More informationGreen-Schwarz action for Type IIA strings on AdS 4 CP 3
MIT-CTP-nnnn Imperial/TP/2-08/nn arxiv:0806.4948v2 [hep-th] 18 Aug 2008 Green-Schwarz action for Type IIA strings on AdS 4 CP 3 B. Stefański, jr. 1,2 1 Center for Theoretical Physics Laboratory for Nuclear
More informationAnomalous Strong Coupling
Simons Center for Geometry and Physics, Stony Brook based on [Brenno Carlini Vallilo, LM, arxiv:1102.1219 [hep-th] ] for a pedagogical review, [LM, arxiv:1104.2604][hep-th] ] XI Workshop on Nonperturbative
More informationType IIB superstring action in AdS 5 S 5 background
FIAN/TD/98-21 Imperial/TP/97-98/44 NSF-ITP-98-055 hep-th/9805028 arxiv:hep-th/9805028v4 11 Jun 1998 Type IIB superstring action in AdS 5 S 5 background R.R. Metsaev a, and A.A. Tseytlin a,b,c, a Department
More informationThere has been great interest recently in type IIB theory on ads 5 S 5 ë1, 2, 3ë, due to its possible relation to N=4,d=4 Yang-Mills theory. This vacu
SLAC-PUB-7840 SU-ITP-98è36 May 1998 Near Horizon Superspace Renata Kallosh 1a, J. Rahmfeld 1b 12 cd and Arvind Rajaraman 1 Department of Physics, Stanford University, Stanford, CA 94305-4060 2 Stanford
More informationSeminar in Wigner Research Centre for Physics. Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013
Seminar in Wigner Research Centre for Physics Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013 Introduction - Old aspects of String theory - AdS/CFT and its Integrability String non-linear sigma
More informationIntroduction Calculation in Gauge Theory Calculation in String Theory Another Saddle Point Summary and Future Works
Introduction AdS/CFT correspondence N = 4 SYM type IIB superstring Wilson loop area of world-sheet Wilson loop + heavy local operator area of deformed world-sheet Zarembo s solution (1/2 BPS Wilson Loop)
More informationarxiv:hep-th/ v1 28 Jan 1999
N=1, D=10 TENSIONLESS SUPERBRANES II. 1 arxiv:hep-th/9901153v1 28 Jan 1999 P. Bozhilov 2 Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia We consider a model for tensionless (null)
More informationSnyder noncommutative space-time from two-time physics
arxiv:hep-th/0408193v1 25 Aug 2004 Snyder noncommutative space-time from two-time physics Juan M. Romero and Adolfo Zamora Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Apartado
More informationSuperstring in the plane-wave background with RR-flux as a conformal field theory
0th December, 008 At Towards New Developments of QFT and Strings, RIKEN Superstring in the plane-wave background with RR-flux as a conformal field theory Naoto Yokoi Institute of Physics, University of
More informationTowards solution of string theory in AdS3 x S 3
Towards solution of string theory in AdS3 x S 3 Arkady Tseytlin based on work with Ben Hoare: arxiv:1303.1037, 1304.4099 Introduction / Review S-matrix for string in AdS3 x S3 x T4 with RR and NSNS flux
More informationAnomalous dimensions at strong coupling
Anomalous dimensions at strong coupling Luca Mazzucato Simons Center for Geometry and Physics Stony Brook University Stony Brook, US NY 11794-3636 Brenno Carlini Vallilo Departamento de Ciencias Físicas,
More informationYangian symmetry in deformed WZNW models on squashed spheres
seminar@ipmu, 2011/05/24 Yangian symmetry in deformed WZNW models on squashed spheres Kentaroh Yoshida (Kyoto Univ.) Based on I. Kawaguchi, D. Orlando and K.Y., arxiv: 1104.0738. I. Kawaguchi and K.Y.,
More informationPoisson-Lie T-Duality and supermanifolds
Poisson-Lie T-Duality and supermanifolds L. Hlavatý, I. Petr, V. Štěpán, J. Vysoký Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague IPM
More informationKentaroh Yoshida (Kyoto Univ.)
2014/03/04 ``Progress in the synthesis of integrabilities arising from gauge string duality Recent progress on q deformations of the AdS 5 5 x S superstring Kentaroh Yoshida (Kyoto Univ.) In collaboration
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 02: String theory
More informationRepresentation of Spin Group Spin(p, q)
Commun. Theor. Phys. Beijing China 48 2007 pp. 415 424 c nternational Academic Publishers Vol. 48 No. 3 September 15 2007 Representation of Spin Group Spinp q WANG Na 1 WU Ke 12 ZHANG Bo 1 1 School of
More information1 Polyakov path integral and BRST cohomology
Week 7 Reading material from the books Polchinski, Chapter 3,4 Becker, Becker, Schwartz, Chapter 3 Green, Schwartz, Witten, chapter 3 1 Polyakov path integral and BRST cohomology We need to discuss now
More informationGRANGIAN QUANTIZATION OF THE HETEROTIC STRING IN THE BOSONIC FORMULAT
September, 1987 IASSNS-HEP-87/draft GRANGIAN QUANTIZATION OF THE HETEROTIC STRING IN THE BOSONIC FORMULAT J. M. F. LABASTIDA and M. PERNICI The Institute for Advanced Study Princeton, NJ 08540, USA ABSTRACT
More informationA New Integrable Couplings of Classical-Boussinesq Hierarchy with Self-Consistent Sources
Commun. Theor. Phys. Beijing, China 54 21 pp. 1 6 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 1, July 15, 21 A New Integrable Couplings of Classical-Boussinesq Hierarchy with Self-Consistent
More informationHelicity conservation in Born-Infeld theory
Helicity conservation in Born-Infeld theory A.A.Rosly and K.G.Selivanov ITEP, Moscow, 117218, B.Cheryomushkinskaya 25 Abstract We prove that the helicity is preserved in the scattering of photons in the
More informationAmplitudes & Wilson Loops at weak & strong coupling
Amplitudes & Wilson Loops at weak & strong coupling David Skinner - Perimeter Institute Caltech - 29 th March 2012 N=4 SYM, 35 years a!er Twistor space is CP 3, described by co-ords It carries a natural
More informationContact interactions in string theory and a reformulation of QED
Contact interactions in string theory and a reformulation of QED James Edwards QFT Seminar November 2014 Based on arxiv:1409.4948 [hep-th] and arxiv:1410.3288 [hep-th] Outline Introduction Worldline formalism
More informationScaling and integrability from AdS 5 S 5
Scaling and integrability from AdS 5 S 5 Riccardo Ricci Imperial College London DAMTP Cambridge 14th October Work in collaboration with S. Giombi, R.Roiban, A. Tseytlin and C.Vergu Outline Introduction
More informationCoordinate/Field Duality in Gauge Theories: Emergence of Matrix Coordinates
Coordinate/Field Duality in Gauge Theories: Emergence of Matrix Coordinates Amir H. Fatollahi Department of Physics, Alzahra University, P. O. Box 19938, Tehran 91167, Iran fath@alzahra.ac.ir Abstract
More informationCitation for published version (APA): Halbersma, R. S. (2002). Geometry of strings and branes. Groningen: s.n.
University of Groningen Geometry of strings and branes Halbersma, Reinder Simon IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please
More informationSome applications of light-cone superspace
Some applications of light-cone superspace Stefano Kovacs (Trinity College Dublin & Dublin Institute for Advanced Studies) Strings and Strong Interactions LNF, 19/09/2008 N =4 supersymmetric Yang Mills
More informationHolographic Wilsonian Renormalization Group
Holographic Wilsonian Renormalization Group JiYoung Kim May 0, 207 Abstract Strongly coupled systems are difficult to study because the perturbation of the systems does not work with strong couplings.
More informationAn overview of branes in the plane wave background
An overview of branes in the plane wave background Kostas Skenderis and Marika Taylor Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018XE Amsterdam, The Netherlands
More informationTalk at the International Workshop RAQIS 12. Angers, France September 2012
Talk at the International Workshop RAQIS 12 Angers, France 10-14 September 2012 Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry V.K. Dobrev Nucl. Phys.
More informationSupertwistors, Chern-Simons And Super Gauge Theories
Supertwistors, Chern-Simons And Super Gauge Theories INSTITUT FÜR THEORETISCHE PHYSIK UNIVERSITÄT HANNOVER From Twistors To Amplitudes, QMUL, London 2005 Contents 1 Motivation Double Fibrations Twistor
More informationBFT embedding of noncommutative D-brane system. Abstract
SOGANG-HEP 271/00 BFT embedding of noncommutative D-brane system Soon-Tae Hong,WonTaeKim, Young-Jai Park, and Myung Seok Yoon Department of Physics and Basic Science Research Institute, Sogang University,
More informationTESTING ADS/CFT. John H. Schwarz STRINGS 2003
TESTING ADS/CFT John H. Schwarz STRINGS 2003 July 6, 2003 1 INTRODUCTION During the past few years 1 Blau et al. constructed a maximally supersymmetric plane-wave background of type IIB string theory as
More informationarxiv: v2 [hep-th] 22 Aug 2011
KEK-TH-1486 KUNS-2354 arxiv:1107.4673v2 hep-th] 22 Aug 2011 Super Yangian of superstring on AdS 5 S 5 revisited Machiko Hatsuda a and Kentaroh Yoshida b Physics Department, Juntendo University, 270-1695,
More informationTwistors and Conformal Higher-Spin. Theory. Tristan Mc Loughlin Trinity College Dublin
Twistors and Conformal Higher-Spin Tristan Mc Loughlin Trinity College Dublin Theory Based on work with Philipp Hähnel & Tim Adamo 1604.08209, 1611.06200. Given the deep connections between twistors, the
More informationRECENT DEVELOPMENTS IN STRING THEORY International Conference Ascona, July Quantum spectral curve of N=4 SYM and its BFKL limit
RECENT DEVELOPMENTS IN STRING THEORY International Conference Ascona, 21 25 July 2014 Quantum spectral curve of N=4 SYM and its BFKL limit Vladimir Kazakov (ENS, Paris) Collaborations with: Nikolay Gromov
More informationHIGHER SPIN PROBLEM IN FIELD THEORY
HIGHER SPIN PROBLEM IN FIELD THEORY I.L. Buchbinder Tomsk I.L. Buchbinder (Tomsk) HIGHER SPIN PROBLEM IN FIELD THEORY Wroclaw, April, 2011 1 / 27 Aims Brief non-expert non-technical review of some old
More informationExact Quantization of a Superparticle in
21st October, 2010 Talk at SFT and Related Aspects Exact Quantization of a Superparticle in AdS 5 S 5 Tetsuo Horigane Institute of Physics, Univ. of Tokyo(Komaba) Based on arxiv : 0912.1166( Phys.Rev.
More informationarxiv:hep-th/ v1 7 Nov 1998
SOGANG-HEP 249/98 Consistent Dirac Quantization of SU(2) Skyrmion equivalent to BFT Scheme arxiv:hep-th/9811066v1 7 Nov 1998 Soon-Tae Hong 1, Yong-Wan Kim 1,2 and Young-Jai Park 1 1 Department of Physics
More informationScattering amplitudes and AdS/CFT
Scattering amplitudes and AdS/CFT Cristian Vergu Brown University BOX 1843 Providence, RI 02912 1 Introduction and notation Scattering amplitudes in the maximally supersymmetric N = 4 gauge theory are
More informationExact spectral equations in planar N=4 SYM theory
Euler Symposium on Theoretical and Mathematical Physics Euler International Mathematical Institute, St. Petersburg, July 12-17, 2013 Exact spectral equations in planar N=4 SYM theory Vladimir Kazakov (ENS,
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v2 23 Feb 2004 100871 Beijing, China Abstract In this paper, complex
More informationarxiv:hep-th/ v3 4 May 2004
SL(2; R) Duality of the Noncommutative DBI Lagrangian Davoud Kamani Institute for Studies in Theoretical Physics and Mathematics (IPM) P.O.Box: 9395-553, Tehran, Iran e-mail: kamani@theory.ipm.ac.ir arxiv:hep-th/0207055v3
More informationarxiv:hep-th/ v1 15 Aug 2000
hep-th/0008120 IPM/P2000/026 Gauged Noncommutative Wess-Zumino-Witten Models arxiv:hep-th/0008120v1 15 Aug 2000 Amir Masoud Ghezelbash,,1, Shahrokh Parvizi,2 Department of Physics, Az-zahra University,
More informationarxiv: v1 [hep-th] 30 Jan 2009
ITP-UU-09-05 SPIN-09-05 TCD-MATH-09-06 HMI-09-03 arxiv:0901.4937v1 [hep-th] 30 Jan 2009 Foundations of the AdS 5 S 5 Superstring Part I Gleb Arutyunov a and Sergey Frolov b a Institute for Theoretical
More informationSmooth Wilson Loops and Yangian Symmetry in Planar N = 4 SYM
Smooth Wilson Loops and Yangian Symmetry in Planar N = 4 SYM ITP, Niklas Beisert Workshop on Hidden symmetries and integrability methods in super Yang Mills theories and their dual string theories Centre
More informationSupertwistors, Super Yang-Mills Theory and Integrability
Supertwistors, Super Yang-Mills Theory and Integrability Institut für Theoretische Physik Universität Hannover April 15, 2005 Duke University/UNC Contents 1 Motivation 2 Supertwistor Geometry Penrose-Ward
More informationThéorie des cordes: quelques applications. Cours II: 4 février 2011
Particules Élémentaires, Gravitation et Cosmologie Année 2010-11 Théorie des cordes: quelques applications Cours II: 4 février 2011 Résumé des cours 2009-10: deuxième partie 04 février 2011 G. Veneziano,
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v3 10 Mar 2004 100871 Beijing, China Abstract In this paper, complex
More informationExistence of Antiparticles as an Indication of Finiteness of Nature. Felix M. Lev
Existence of Antiparticles as an Indication of Finiteness of Nature Felix M. Lev Artwork Conversion Software Inc., 1201 Morningside Drive, Manhattan Beach, CA 90266, USA (Email: felixlev314@gmail.com)
More informationQuantum Field Theory III
Quantum Field Theory III Prof. Erick Weinberg January 19, 2011 1 Lecture 1 1.1 Structure We will start with a bit of group theory, and we will talk about spontaneous symmetry broken. Then we will talk
More informationLOCALIZATION OF FIELDS ON A BRANE IN SIX DIMENSIONS.
LOCALIZATION OF FIELDS ON A BRANE IN SIX DIMENSIONS Merab Gogberashvili a and Paul Midodashvili b a Andronikashvili Institute of Physics, 6 Tamarashvili Str., Tbilisi 3877, Georgia E-mail: gogber@hotmail.com
More informationAndrei Mikhailov. July 2006 / Potsdam
Poisson Andrei Mikhailov California Institute of Technology July 2006 / Potsdam Poisson brackets are very important in classical mechanics, in particular because they are the classical analogue of the
More informationA New Formalism of Arbitrary Spin Particle Equations. Abstract
A New Formalism of Arbitrary Spin Particle Equations S.R. Shi Huiyang Radio and TV station,daishui,huiyang,huizhou,guangdong,china,56 (Dated: October 4, 6) Abstract In this paper, a new formalism of arbitrary
More informationLarge Spin Strings in AdS 3
UTTG-15-0 CERN-TH/00-367 hep-th/01147 Large Spin Strings in AdS 3 Amit Loewy a and Yaron Oz b,c a Department of Physics, University of Texas, Austin, TX 7871 b School of Physics and Astronomy, Raymond
More informationThe Geometry of two dimensional Supersymmetric Nonlinear σ Model
The Geometry of two dimensional Supersymmetric Nonlinear σ Model Hao Guo March 14, 2005 Dept. of Physics, University of Chicago Abstract In this report, we investigate the relation between supersymmetry
More informationOn Type II strings in exact superconformal non-constant RR backgrounds
arxiv:hep-th/0301089v Jan 003 ULB-TH/03-04 On Type II strings in exact superconformal non-constant RR backgrounds Giulio Bonelli 1 Physique Theorique et Mathematique - Universite Libre de Bruxelles Campus
More informationCharacteristic Numbers of Matrix Lie Algebras
Commun. Theor. Phys. (Beijing China) 49 (8) pp. 845 85 c Chinese Physical Society Vol. 49 No. 4 April 15 8 Characteristic Numbers of Matrix Lie Algebras ZHANG Yu-Feng 1 and FAN En-Gui 1 Mathematical School
More informationExercise 1 Classical Bosonic String
Exercise 1 Classical Bosonic String 1. The Relativistic Particle The action describing a free relativistic point particle of mass m moving in a D- dimensional Minkowski spacetime is described by ) 1 S
More informationTwistor Strings, Gauge Theory and Gravity. Abou Zeid, Hull and Mason hep-th/
Twistor Strings, Gauge Theory and Gravity Abou Zeid, Hull and Mason hep-th/0606272 Amplitudes for YM, Gravity have elegant twistor space structure: Twistor Geometry Amplitudes for YM, Gravity have elegant
More informationIntegrability of spectrum of N=4 SYM theory
Todai/Riken joint workshop on Super Yang-Mills, solvable systems and related subjects University of Tokyo, October 23, 2013 Integrability of spectrum of N=4 SYM theory Vladimir Kazakov (ENS, Paris) Collaborations
More informationLecture 8: 1-loop closed string vacuum amplitude
Lecture 8: 1-loop closed string vacuum amplitude José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 5, 2013 José D. Edelstein (USC) Lecture 8: 1-loop vacuum
More informationTechniques for exact calculations in 4D SUSY gauge theories
Techniques for exact calculations in 4D SUSY gauge theories Takuya Okuda University of Tokyo, Komaba 6th Asian Winter School on Strings, Particles and Cosmology 1 First lecture Motivations for studying
More informationChern-Simons Theories and AdS/CFT
Chern-Simons Theories and AdS/CFT Igor Klebanov PCTS and Department of Physics Talk at the AdS/CMT Mini-program KITP, July 2009 Introduction Recent progress has led to realization that coincident membranes
More informationLecture 9: RR-sector and D-branes
Lecture 9: RR-sector and D-branes José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 6, 2013 José D. Edelstein (USC) Lecture 9: RR-sector and D-branes 6-mar-2013
More informationDifferential Representations of SO(4) Dynamical Group
Commun. Theor. Phys. Beijing China 50 2008 pp. 63 68 c Chinese Physical Society Vol. 50 No. July 5 2008 Differential Representations of SO4 Dynamical Group ZHAO Dun WANG Shun-Jin 2 and LUO Hong-Gang 34
More informationYangian Symmetry of Planar N = 4 SYM
Yangian Symmetry of Planar N = 4 SYM ITP, Niklas Beisert New formulations for scattering amplitudes Ludwig Maximilians Universität, München 9 September 2016 work with J. Plefka, D. Müller, C. Vergu (1509.05403);
More informationUnification of twistors and Ramond vectors: transmutation of superconformal boosts into local supersymmetry
Unification of twistors and Ramond vectors: transmutation of superconformal boosts into local supersymmetry arxiv:0707.3453v1 [hep-th] 23 Jul 2007 A.A. Zheltukhin Kharkov Institute of Physics and Technology,
More informationAll the fundamental massless fields in bosonic string theory
Early View publication on wileyonlinelibrary.com (issue and page numbers not yet assigned; citable using Digital Object Identifier DOI) Fortschr. Phys., 8 (0) / DOI 0.00/prop.000003 All the fundamental
More informationIntroduction to Group Theory
Chapter 10 Introduction to Group Theory Since symmetries described by groups play such an important role in modern physics, we will take a little time to introduce the basic structure (as seen by a physicist)
More informationSpinning strings and QED
Spinning strings and QED James Edwards Oxford Particles and Fields Seminar January 2015 Based on arxiv:1409.4948 [hep-th] and arxiv:1410.3288 [hep-th] Outline Introduction Various relationships between
More informationProblem Set 1 Classical Worldsheet Dynamics
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics String Theory (8.821) Prof. J. McGreevy Fall 2007 Problem Set 1 Classical Worldsheet Dynamics Reading: GSW 2.1, Polchinski 1.2-1.4. Try 3.2-3.3.
More informationIntroduction to string theory 2 - Quantization
Remigiusz Durka Institute of Theoretical Physics Wroclaw / 34 Table of content Introduction to Quantization Classical String Quantum String 2 / 34 Classical Theory In the classical mechanics one has dynamical
More informationLectures on Gamma Matrix and Supersymmetry
Lectures on Gamma Matrix and Supersymmetry Jeong-Hyuck Park Physics Department, Sungkyunkwan University Chunchun-dong, Jangan-gu, Suwon 440-746, Korea Abstract This lecture note surveys the Gamma matrix
More informationYangians In Deformed Super Yang-Mills Theories
Yangians In Deformed Super Yang-Mills Theories arxiv:0802.3644 [hep-th] JHEP 04:051, 2008 Jay N. Ihry UNC-CH April 17, 2008 Jay N. Ihry UNC-CH Yangians In Deformed Super Yang-Mills Theories arxiv:0802.3644
More informationComplex frequencies of a massless scalar field in loop quantum black hole spacetime
Complex frequencies of a massless scalar field in loop quantum black hole spacetime Chen Ju-Hua( ) and Wang Yong-Jiu( ) College of Physics and Information Science, Key Laboratory of Low Dimensional Quantum
More informationAdS/CFT duality, spin chains and 2d effective actions
AdS/CFT duality, spin chains and 2d effective actions R. Roiban, A. Tirziu and A. A. Tseytlin Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2-d actions, hep-th/0604199 also talks
More informationIntroduction to Modern Quantum Field Theory
Department of Mathematics University of Texas at Arlington Arlington, TX USA Febuary, 2016 Recall Einstein s famous equation, E 2 = (Mc 2 ) 2 + (c p) 2, where c is the speed of light, M is the classical
More informationVector Supersymmetry and Non-linear Realizations 1
1 Based on R. Casalbuoni, J. Gomis, K. Kamimura and G. Longhi, arxiv:0801.2702, JHEP (2008) R. Casalbuoni, F. Elmetti, J. Gomis, K. Kamimura, L. Tamassia and A. Van Proeyen, arxiv:0812.1982, JHEP (2009)
More informationLecture 10: A (Brief) Introduction to Group Theory (See Chapter 3.13 in Boas, 3rd Edition)
Lecture 0: A (Brief) Introduction to Group heory (See Chapter 3.3 in Boas, 3rd Edition) Having gained some new experience with matrices, which provide us with representations of groups, and because symmetries
More informationGraded Lie Algebra of Quaternions and Superalgebra of SO(3, 1)
Graded Lie Algebra of Quaternions and Superalgebra of SO3, 1 Bhupendra C. S. Chauhan, O. P. S. Negi October 22, 2016 Department of Physics Kumaun University S. S. J. Campus Almora 263601 Uttarakhand Email:
More informationLorentz-covariant spectrum of single-particle states and their field theory Physics 230A, Spring 2007, Hitoshi Murayama
Lorentz-covariant spectrum of single-particle states and their field theory Physics 30A, Spring 007, Hitoshi Murayama 1 Poincaré Symmetry In order to understand the number of degrees of freedom we need
More informationInheritance principle and Non-renormalization theorems at finite temperature
hep-th/0509117 MIT-CTP-3679 arxiv:hep-th/0509117v2 19 Sep 2005 Inheritance principle and Non-renormalization theorems at finite temperature Mauro Brigante 1, Guido Festuccia 1,2 and Hong Liu 1,2 1 Center
More informationarxiv:hep-th/ v1 21 Feb 2006
Spinor field realizations of the non-critical W 2,4 string based on the linear W 1,2,4 algebra Zhang Li-Jie 1 and Liu Yu-Xiao 2 1 Department of Mathematics and Physics, Dalian Jiaotong University, Dalian
More informationSpectrum of Holographic Wilson Loops
Spectrum of Holographic Wilson Loops Leopoldo Pando Zayas University of Michigan Continuous Advances in QCD 2011 University of Minnesota Based on arxiv:1101.5145 Alberto Faraggi and LPZ Work in Progress,
More informationThe N = 2 Gauss-Bonnet invariant in and out of superspace
The N = 2 Gauss-Bonnet invariant in and out of superspace Daniel Butter NIKHEF College Station April 25, 2013 Based on work with B. de Wit, S. Kuzenko, and I. Lodato Daniel Butter (NIKHEF) Super GB 1 /
More informationEmergent Quantum Criticality
(Non-)Fermi Liquids and Emergent Quantum Criticality from gravity Hong Liu Massachusetts setts Institute te of Technology HL, John McGreevy, David Vegh, 0903.2477 Tom Faulkner, HL, JM, DV, to appear Sung-Sik
More informationLiouville Theory and the S 1 /Z 2 orbifold
Liouville Theory and the S 1 /Z 2 Orbifold Supervised by Dr Umut Gursoy Polyakov Path Integral Using Polyakov formalism the String Theory partition function is: Z = DgDX exp ( S[X; g] µ 0 d 2 z ) g (1)
More informationarxiv:hep-th/ v3 24 Apr 2007
Anti-de Sitter boundary in Poincaré coordinates C. A. Ballón Bayona and Nelson R. F. Braga Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 Brazil Abstract
More informationBoundary States in IIA Plane-Wave Background
hep-th/368 Boundary States in IIA Plane-Wave Background arxiv:hep-th/368v 7 Jun 3 Yeonjung Kim, a and Jaemo Park b a epartment of Physics, KAIST, Taejon 35-7, Korea b epartment of Physics, POSTECH, Pohang
More informationOff-shell conformal supergravity in 3D
School of Physics, The University of Western Australia, ARC DECRA fellow ANZAMP meeting, Mooloolaba, 28 November 2013 Based on: Kuzenko & GTM, JHEP 1303, 113 (2013), 1212.6852 Butter, Kuzenko, Novak &
More informationCurrent Superalgebra and Twisted Conformal Field Theory
Commun. Theor. Phys. Beijing, China 47 007 pp. 69 77 c International Academic Publishers Vol. 47, No. 1, January 15, 007 On gl Current Superalgebra and Twisted Conformal Field Theory DING Xiang-Mao, 1,
More informationA Study on Kac-Moody Superalgebras
ICGTMP, 2012 Chern Institute of Mathematics, Tianjin, China Aug 2o-26, 2012 The importance of being Lie Discrete groups describe discrete symmetries. Continues symmetries are described by so called Lie
More informationSuper-(dS+AdS) and double Super-Poincare
Lomonosov Moscow State University, Skobelsyn Institute of Nuclear Physics, 119 992 Moscow, Russia International Workshop: Supersymmetry in Integrable Systems - SIS 14 Joint Institute for Nuclear Research,
More informationSpiky strings, light-like Wilson loops and a pp-wave anomaly
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arxiv:080.039 A. Tseytlin, M.K. arxiv:0804.3438 R. Ishizeki, A. Tirziu, M.K. Summary Introduction
More informationIntegrable structure of various melting crystal models
Integrable structure of various melting crystal models Kanehisa Takasaki, Kinki University Taipei, April 10 12, 2015 Contents 1. Ordinary melting crystal model 2. Modified melting crystal model 3. Orbifold
More informationin collaboration with K.Furuta, M.Hanada and Y.Kimura. Hikaru Kawai (Kyoto Univ.) There are several types of matrix models, but here for the sake of
Curved space-times and degrees of freedom in matrix models 1 Based on hep-th/0508211, hep-th/0602210 and hep-th/0611093 in collaboration with K.Furuta, M.Hanada and Y.Kimura. Hikaru Kawai (Kyoto Univ.)
More informationConnecting the ambitwistor and the sectorized heterotic strings
Connecting the ambitwistor and the sectorized heterotic strings Renann Lipinski Jusinskas February 11th - 2018 Discussion Meeting on String Field Theory and String Phenomenology - HRI, Allahabad, India
More information