Affine SU(N) algebra from wall-crossings
|
|
- Hilda Elliott
- 5 years ago
- Views:
Transcription
1 Affine SU(N) algebra from wall-crossings Takahiro Nishinaka ( KEK ) arxiv: : T. N. and Satoshi Yamaguchi 12 Aug. 2011
2 Counting BPS D-branes on CY3 Microstates of black holes in R 4 Instanton counting on D-branes Topological string Quiver gauge theory, Brane tilings Wall-crossing phenomena
3 Counting BPS D-branes on CY3 Microstates of black holes in R 4 Instanton counting on D-branes Topological string Quiver gauge theory, Brane tilings Wall-crossing phenomena
4 D4-D2-D0 on CY3 D4-D2-D0 bound states on CY3 # D-brane bound states? 6-dim ( Calabi-Yau ) The degeneracy of BPS D-branes depends on the moduli parameters = D2/D0 branes on a single D4 sizes and B-fields of compact cycles 4-dim ( R 4 ) BPS particle Wall-crossing phenomena N =2 supersymmetry
5 D4-D2-D0 on CY3 Large radii limit D0-brane D2-brane instanton on D4 magnetic flux on D4 Chern-Simons interaction on D4 D4 D0-charge = # instantons C (1) F F Q 0 = 1 F F, 8π 2 D4 D2-charge = # magnetic flux C (3) F Q 2 = 1 F k, 2π k : unit volume form on 2-cycle
6 ALE instantons If a D4-brane is wrapped on ALE space... A N 1 -ALE space: minimal resolution of C 2 /Z N (z 1,z 2 ) blowup (0, 0) N 1 (z 1,z 2 ) (ωz 1, ωz 2 ) where ω = e 2πi/N The instanton partition function on a D4-brane wrapping A N 1 ALE space = character of affine SU(N) algebra [Nakajima] [Vafa-Witten]
7 ALE instantons Affine SU(N) character q Q : Boltzmann weight of D0 : Boltzmann weight of D2 χ csu(n) 1 r = 1 η(q) N 1 n 1,,n N 1 Z q P N 1 i=1 n2 i P N 2 i=1 n in i+1 +n 1 r+ r2 2 N 1 N N 1 j=1 n Q j + N i j N r ex.) affine SU(2) χ csu(2) 1 r = 1 η(q) n= q n2 +nr+ r2 4 Q n+ r 2
8 What in this talk? Relation between ALE instantons and D4-D2-D0 wall-crossings
9 ALE C A N 1 -ALE C D A N 1 -ALE space (D) β 1 β 2 β N N 1 N A single D4-brane wrapped on D moduli D2-branes wrapped on β 1 β N 1 : N 1 blowup two-cycles D0-branes localized in CY3 = B-fields and radii of β 1 β N 1
10 Outline of the rest of this talk 1. Wall-crossings in d=4, N=2 SUSY theory 2. Apply it to our case. 3. Summary
11 Wall-crossings in d=4, N=2 SUSY theory
12 Wall-crossing of BPS states BPS index The trace is taken over all one-particle states with charge. Γ Ω(Γ; z) := 1 2 Tr Γ[( 1) 2J (2J) 2 ] This index is piecewise constant in the moduli space of vacua, but not globally constant. z ( : vacuum moduli parameters ) = # bosonic BPS multiplets # fermionic BPS multiplets Wall-crossing phenomena moduli space z discrete change Ω(Γ; z 1 ) Ω(Γ; z 2 ) Some decay BPS BPS BPS Γ Γ 1 + Γ 2 occurs. wall of marginal stability
13 Wall-crossing of BPS states So the moduli space is divided into chambers by the walls of marginal stability. z jump jump jump jump jump Ω(Γ,z 2 ) Ω(Γ,z 3 ) Ω(Γ,z 4 ) Ω(Γ,z 5 ) Ω(Γ,z 1 ) Ω(Γ,z 6 ) wall wall wall wall wall The BPS index is exactly constant in each chamber.
14 Wall-crossing of BPS states Semi-primitive wall-crossing formula Γ : primitive There is no positive integer that can divide out Γ. ( except for one ) Suppose the wall-crossing is associated to a BPS decay channel Γ Γ 1 + nγ 2, n N where Γ 1, Γ 2 are primitive. Then the BPS partition function behaves as Z Z (1 + ( 1) jγ2,γ e jγ 2 ) ±jγ 2,ΓΩ(jΓ 2 ) [Denef-Moore] j=1 [Kontsevich-Soibelman] through the wall-crossing. Here we defined Z = Γ Ω(Γ; z)e Γ, e Γ 1 e Γ 2 = e Γ 1+Γ 2 partition function Boltzmann weight
15 Apply it to our case!
16 ALE C (D) Wall-crossing? β 1 β 2 β N 1 For Γ = D4 + k i D2 (i) + ld0, possible decays are 1 2 N 1 N Γ Γ 1 + Γ 2 Γ 2 = m i D2 (i) + nd0 (Γ 1 = Γ Γ 2 ) (m i = ±1) Γ 2, Γ =0 There is no wall-crossing!! cf) wall-crossing formula Z Z (1 + ( 1) jγ2,γ e jγ 2 ) ±jγ 2,ΓΩ(jΓ 2 ) j=1
17 Add dummy cycle Dummy cycle and flops We add a dummy two-cycle. In the large radius limit of β 0, we should recover the original CY3. β 0 β 1 β 2 (D) β N 1 Now, we have a non-vanishing intersection product: β 0, D =1 1 2 N 1 N Non-trivial wall-crossings!
18 Add dummy cycle ex.) -ALE A 1 C D4 is wrapped on A 1 -ALE space β 1 1 2
19 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C (0 < Im z 0 ) moduli parameters β 0 z 0 β 1 z 1 z 0,z 1 C 1 2 Im z i area of i-th cycle
20 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C (0 < Im z 0 ) moduli parameters z 0,z 1 z 0 z 1 Im zi area of i-th cycle C 1 2
21 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C 1 2 moduli parameters z 0,z 1 C Im z i area of i-th cycle
22 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C moduli parameters D4 is wrapped on O( 1) P 1 z 0 z 1 2 Im z i z 0,z 1 C area of i-th cycle 1 z 0 = z 0, z 1 = z 0 + z 1
23 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C moduli parameters D4 is wrapped on O( 1) P 1 z 0 z 1 2 z 0,z 1 C Im z i area of i-th cycle 1 z 0 = z 0, z 1 = z 0 + z 1
24 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C moduli parameters z 0,z 1 C 2 Im z i area of i-th cycle 1
25 Add dummy cycle Im z 1 0 Im z 0 ex.) -ALE A 1 C D4 is wrapped on C 2 z 0 z moduli parameters Im z i z 0,z 1 C area of i-th cycle z 0 = z 1, z 1 = z 0 z 1
26 Im z 0 =+ (large radii) Z + z 0 Walls of MS Γ Γ 1 + Γ 2 Γ = D4 + l i D2 (i) + kd0 0 W m0,m 1 n : Γ 2 = i=0,1 m i D2 (i) + nd0 Im z 0 = (large radii) Z
27 Im z 0 =+ (large radii) Z + W 1, 1 0 W 1, 1 1 W 1, 1 2 W 1, W +1,0 2 W 1,0 0 W +1,0 1 W +1,0 0 W 1,0 2 z 0 W +1,0 1 W m0,m 1 n : Γ 2 = Walls of MS Γ Γ 1 + Γ 2 Γ = D4 + l i D2 (i) + kd0 i=0,1 m i D2 (i) + nd0 W +1,+1 1 W +1,+1 0 W +1,+1 1 Im z 0 = (large radii) Z
28 Results of wall-crossings Z + Z β 0 β 1 Z = n,m 0,m 1 Ω(D4 + m i D2 (i) + nd0)q n Q 0 m 0 Q 1 m 1 Result of wall-crossing formula Z + = Z n=0 1 n=1 1 q n (1 q n Q 0 )(1 q n Q 0 Q 1 ) m=1 (1 q n Q 0 1 )(1 q m Q 1 0 Q 1 1 )
29 Results of wall-crossings Z + Z Z = β 1 n,m 0,m 1 Ω(D4 + m i D2 (i) + nd0)q n Q 0 m 0 Q 1 m 1 Result of wall-crossing formula Z + = Z n=0 1 n=1 1 q n (1 q n Q 0 )(1 q n Q 0 Q 1 ) m=1 (1 q n Q 0 1 )(1 q m Q 1 0 Q 1 1 ) omit β 0 Z + Q0 independent = 1 1 q n n=1 3 m= q m2 Q 1 m = q1/8 η(q) 2 χcsu(2) 1 0 (q, Q 1 )
30 We can generalize it to A N 1 ALE space!!
31 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
32 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
33 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
34 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
35 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
36 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N
37 Generalization Multiple flops We now have multiplet flop transitions. N 1 N 1 2
38 Generalization Multiple flops We now have multiplet flop transitions. 1 2 N 1 N Instantons on C 2
39 Generalization Affine SU(N) character from wall-crossings wall-crossings Q 0 Z (q, Q) Z + (q, Q) 1 = 1 q n n=1 From the wall-crossing formula, we find N 1 Z + (q, Q) = Z (q, Q) (1 q n Q 0 Q k ) k=0 n=0 m=1 (1 q m Q 1 0 Q 1 k ) = =1 1 1 q N+1 n 0,,n N 1 Z q P N 1 i=0 n i (n i 1) 2 N 1 k=0 ( Q 0 Q k ) n k
40 Generalization Z + (q, Q) = =1 1 1 q N+1 n 0,,n N 1 Z q P N 1 i=0 n i (n i 1) 2 N 1 k=0 ( Q 0 Q k ) n k After removing dummy cycle... Z + (q, Q) Q0 independent = n=1 1 1 q n 2 χ csu(n) 1 0 (q, Q) where χ csu(n) 1 0 (q, Q) = 1 η(q) N 1 n 1,,n N 1 Z q P N 1 N 1 i=1 n2 i P N 2 i=1 n in i+1 j=1 Q j n j Affine SU(N) character is correctly reproduced by wall-crossings!
41 Summary We study the relation between ALE instantons and wall-crossings of D4- D2-D0 on CY3. By adding a dummy cycle, the wall-crossings interpolate the instanton partition functions on ALE space and C 2. Our analysis relies on the wall-crossing formula of d=4, N=2 theories. Future work r χ csu(n) 1 The parameter of is left for future work. r Generalizations to other instanton partition functions on Vafa-Witten theories are to be studied.
42 That s all for my presentation. Thank you very much.
BPS states, Wall-crossing and Quivers
Iberian Strings 2012 Bilbao BPS states, Wall-crossing and Quivers IST, Lisboa Michele Cirafici M.C.& A.Sincovics & R.J. Szabo: 0803.4188, 1012.2725, 1108.3922 and M.C. to appear BPS States in String theory
More informationFree fermion and wall-crossing
Free fermion and wall-crossing Jie Yang School of Mathematical Sciences, Capital Normal University yangjie@cnu.edu.cn March 4, 202 Motivation For string theorists It is called BPS states counting which
More informationCounting black hole microstates as open string flux vacua
Counting black hole microstates as open string flux vacua Frederik Denef KITP, November 23, 2005 F. Denef and G. Moore, to appear Outline Setting and formulation of the problem Black hole microstates and
More informationBPS States in N=4. Ashoke Sen. Harish-Chandra Research Institute, Allahabad, India
BPS States in N=4 Ashoke Sen Harish-Chandra Research Institute, Allahabad, India Caltech, March 2012 Goal: Study the spectrum of BPS states in N=4 supersymmetric SU(n) Yang-Mills theories on the Coulomb
More information2d-4d wall-crossing and hyperholomorphic bundles
2d-4d wall-crossing and hyperholomorphic bundles Andrew Neitzke, UT Austin (work in progress with Davide Gaiotto, Greg Moore) DESY, December 2010 Preface Wall-crossing is an annoying/beautiful phenomenon
More informationWitten Index for Noncompact Dynamics
Witten Index for Noncompact Dynamics PILJIN YI Korea Institute for Advanced Study USTC, Hefei, May 2016 S.J. Lee + P.Y., 2016 K.Hori + H.Kim + P. Y. 2014 Witten Index for Noncompact Dynamics how shall
More informationYet Another Alternative to Compactification by Heterotic Five-branes
The University of Tokyo, Hongo: October 26, 2009 Yet Another Alternative to Compactification by Heterotic Five-branes arxiv: 0905.285 [hep-th] Tetsuji KIMURA (KEK) Shun ya Mizoguchi (KEK, SOKENDAI) Introduction
More informationWeb Formalism and the IR limit of massive 2D N=(2,2) QFT. collaboration with Davide Gaiotto & Edward Witten
Web Formalism and the IR limit of massive 2D N=(2,2) QFT -or - A short ride with a big machine SCGP, Nov. 17, 2014 Gregory Moore, Rutgers University collaboration with Davide Gaiotto & Edward Witten draft
More informationYet Another Alternative to Compactification
Okayama Institute for Quantum Physics: June 26, 2009 Yet Another Alternative to Compactification Heterotic five-branes explain why three generations in Nature arxiv: 0905.2185 [hep-th] Tetsuji KIMURA (KEK)
More informationOrientiholes Γ 2 Γ 1. Frederik Denef, Mboyo Esole and Megha Padi, arxiv:
Orientiholes Γ 2 Γ 1 Γ 0 Γ 1 Γ 2 Frederik Denef, Mboyo Esole and Megha Padi, arxiv:0901.2540 Outline Motivation and basic idea Review of N = 2 black hole bound states Type IIA orientiholes Motivation and
More informationKnot Homology from Refined Chern-Simons Theory
Knot Homology from Refined Chern-Simons Theory Mina Aganagic UC Berkeley Based on work with Shamil Shakirov arxiv: 1105.5117 1 the knot invariant Witten explained in 88 that J(K, q) constructed by Jones
More informationGauge Threshold Corrections for Local String Models
Gauge Threshold Corrections for Local String Models Stockholm, November 16, 2009 Based on arxiv:0901.4350 (JC), 0906.3297 (JC, Palti) Local vs Global There are many different proposals to realise Standard
More informationF-theory effective physics via M-theory. Thomas W. Grimm!! Max Planck Institute for Physics (Werner-Heisenberg-Institut)! Munich
F-theory effective physics via M-theory Thomas W. Grimm Max Planck Institute for Physics (Werner-Heisenberg-Institut) Munich Ahrenshoop conference, July 2014 1 Introduction In recent years there has been
More information5d SCFTs and instanton partition functions
5d SCFTs and instanton partition functions Hirotaka Hayashi (IFT UAM-CSIC) Hee-Cheol Kim and Takahiro Nishinaka [arxiv:1310.3854] Gianluca Zoccarato [arxiv:1409.0571] Yuji Tachikawa and Kazuya Yonekura
More informationFixing all moduli in F-theory and type II strings
Fixing all moduli in F-theory and type II strings 0504058 Per Berglund, P.M. [0501139 D. Lüst, P.M., S. Reffert, S. Stieberger] 1 - Flux compactifications are important in many constructions of string
More informationwall crossing redux PILJIN YI STRINGS 2013 KOREA INSTITUTE for ADVANCED STUDY
wall crossing redux PILJIN YI KOREA INSTITUTE for ADVANCED STUDY STRINGS 2013 2008 Kontsevich+Soibelman 2008/2009/2010/2011/2012 Gaiotto+Moore+Neitzke 2007/2009 Derksen+Weyman+Zelevinsky 2011 Keller 2011
More informationSurface Defects and the BPS Spectrum of 4d N=2 Theories
Surface Defects and the BPS Spectrum of 4d N=2 Theories Solvay Conference, May 19, 2011 Gregory Moore, Rutgers University Davide Gaiotto, G.M., Andy Neitzke Wall-crossing in Coupled 2d-4d Systems: 1103.2598
More informationAnomalous discrete symmetries in D-brane models
Anomalous discrete symmetries in D-brane models Shohei Uemura Maskawa Institute for Science and Culture, Kyoto Sangyo University based on a work in progress with Tatsuo Kobayashi (Hokkaido University),
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationDualities and Topological Strings
Dualities and Topological Strings Strings 2006, Beijing - RD, C. Vafa, E.Verlinde, hep-th/0602087 - work in progress w/ C. Vafa & C. Beasley, L. Hollands Robbert Dijkgraaf University of Amsterdam Topological
More informationBlack Hole Microstate Counting using Pure D-brane Systems
Black Hole Microstate Counting using Pure D-brane Systems HRI, Allahabad, India 11.19.2015 UC Davis, Davis based on JHEP10(2014)186 [arxiv:1405.0412] and upcoming paper with Abhishek Chowdhury, Richard
More informationPart I. Refined Wall-Crossing
Part I Refined Wall-Crossing Chapter Multi-Centered Black Holes and Refined Microstate Counting As explained in the Introduction, BPS indices for Calabi-Yau threefolds can be defined in several different
More informationWall Crossing from Boltzmann Black Hole Halos
Preprint typeset in JHEP style - HYPER VERSION Wall Crossing from Boltzmann Black Hole Halos arxiv:0.58v3 [hep-th] Mar 0 Jan Manschot, Boris Pioline, Ashoke Sen 3 Institut de Physique Théorique, CEA Saclay,
More informationString Phenomenology ???
String Phenomenology Andre Lukas Oxford, Theoretical Physics d=11 SUGRA IIB M IIA??? I E x E 8 8 SO(32) Outline A (very) basic introduction to string theory String theory and the real world? Recent work
More informationInstanton effective action in - background and D3/D(-1)-brane system in R-R background
Instanton effective action in - background and D3/D(-1)-brane system in R-R background Speaker : Takuya Saka (Tokyo Tech.) Collaboration with Katsushi Ito, Shin Sasaki (Tokyo Tech.) And Hiroaki Nakajima
More informationRefined BPS Indices, Intrinsic Higgs States and Quiver Invariants
Refined BPS Indices, Intrinsic Higgs States and Quiver Invariants ddd (KIAS) USTC 26 Sep 2013 Base on: H. Kim, J. Park, ZLW and P. Yi, JHEP 1109 (2011) 079 S.-J. Lee, ZLW and P. Yi, JHEP 1207 (2012) 169
More informationDavid R. Morrison. String Phenomenology 2008 University of Pennsylvania 31 May 2008
: : University of California, Santa Barbara String Phenomenology 2008 University of Pennsylvania 31 May 2008 engineering has been a very successful approach to studying string vacua, and has been essential
More informationGeneralized N = 1 orientifold compactifications
Generalized N = 1 orientifold compactifications Thomas W. Grimm University of Wisconsin, Madison based on: [hep-th/0602241] Iman Benmachiche, TWG [hep-th/0507153] TWG Madison, Wisconsin, November 2006
More informationD-brane instantons in Type II orientifolds
D-brane instantons in Type II orientifolds in collaboration with R. Blumenhagen, M. Cvetič, D. Lüst, R. Richter Timo Weigand Department of Physics and Astronomy, University of Pennsylvania Strings 2008
More informationGeneralized Kac-Moody Algebras from CHL Dyons
Generalized Kac-Moody Algebras from CHL Dyons Suresh Govindarajan Department of Physics Indian Institute of Technology Madras Talk at CHEP on Sept. 9, 2008 Based on arxiv:0807.4451 with K. Gopala Krishna
More informationA wall-crossing formula for 2d-4d DT invariants
A wall-crossing formula for 2d-4d DT invariants Andrew Neitzke, UT Austin (joint work with Davide Gaiotto, Greg Moore) Cetraro, July 2011 Preface In the last few years there has been a lot of progress
More informationInstantons in string theory via F-theory
Instantons in string theory via F-theory Andrés Collinucci ASC, LMU, Munich Padova, May 12, 2010 arxiv:1002.1894 in collaboration with R. Blumenhagen and B. Jurke Outline 1. Intro: From string theory to
More informationBrane Tilings: NSVZ Beta Function
Brane Tilings: NSVZ Beta Function Amihay Hanany Imperial College & KITP UCSB 1 NSVZ Beta Function 2 NSVZ Beta Function β 1 g 2 = 1 8π 2 3N M µ[r M ](1 γ M (g)) 1 g 2 N/8π 2 2 NSVZ Beta Function β 1 g 2
More informationHeterotic Torsional Backgrounds, from Supergravity to CFT
Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,
More informationEntropy of asymptotically flat black holes in gauged supergravit
Entropy of asymptotically flat black holes in gauged supergravity with Nava Gaddam, Alessandra Gnecchi (Utrecht), Oscar Varela (Harvard) - work in progress. BPS Black Holes BPS Black holes in flat space
More informationWall-crossing from quantum multi-centered BPS black holes
Wall-crossing from quantum multi-centered BPS black holes Boris Pioline LPTHE, Jussieu DAMTP, Cambridge, 27/4/2011 based on work with J. Manschot and A. Sen, arxiv:1011.1258, 1103.0261,1103.1887 Boris
More informationThink Globally, Act Locally
Think Globally, Act Locally Nathan Seiberg Institute for Advanced Study Quantum Fields beyond Perturbation Theory, KITP 2014 Ofer Aharony, NS, Yuji Tachikawa, arxiv:1305.0318 Anton Kapustin, Ryan Thorngren,
More informationTHE MASTER SPACE OF N=1 GAUGE THEORIES
THE MASTER SPACE OF N=1 GAUGE THEORIES Alberto Zaffaroni CAQCD 2008 Butti, Forcella, Zaffaroni hepth/0611229 Forcella, Hanany, Zaffaroni hepth/0701236 Butti,Forcella,Hanany,Vegh, Zaffaroni, arxiv 0705.2771
More informationSpectral Networks and Their Applications. Caltech, March, 2012
Spectral Networks and Their Applications Caltech, March, 2012 Gregory Moore, Rutgers University Davide Gaiotto, o, G.M., Andy Neitzke e Spectral Networks and Snakes, pretty much finished Spectral Networks,
More informationTwo Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges. Adi Armoni Swansea University
Two Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges Adi Armoni Swansea University Queen Mary, April 2009 1 Introduction Seiberg duality (Seiberg 1994) is a highly non-trivial
More informationFramed BPS States In Four And Two Dimensions. Gregory Moore. String Math, Paris, June 27, 2016
Framed BPS States In Four And Two Dimensions Gregory Moore String Math, Paris, June 27, 2016 1 Review Derivation Of KS WCF Using Framed BPS States (with D. Gaiotto & A. Neitzke, 2010, ) 2 3 Interfaces
More informationPartition functions of N = 4 Yang-Mills and applications
Partition functions of N = 4 Yang-Mills and applications Jan Manschot Universität Bonn & MPIM ISM, Puri December 20, 2012 Outline 1. Partition functions of topologically twisted N = 4 U(r) Yang-Mills theory
More informationOn Flux Quantization in F-Theory
On Flux Quantization in F-Theory Raffaele Savelli MPI - Munich Bad Honnef, March 2011 Based on work with A. Collinucci, arxiv: 1011.6388 Motivations Motivations The recent attempts to find UV-completions
More informationFlux Compactification of Type IIB Supergravity
Flux Compactification of Type IIB Supergravity based Klaus Behrndt, LMU Munich Based work done with: M. Cvetic and P. Gao 1) Introduction 2) Fluxes in type IIA supergravity 4) Fluxes in type IIB supergravity
More informationA Landscape of Field Theories
A Landscape of Field Theories Travis Maxfield Enrico Fermi Institute, University of Chicago October 30, 2015 Based on arxiv: 1511.xxxxx w/ D. Robbins and S. Sethi Summary Despite the recent proliferation
More informationLittle strings and T-duality
Little strings and T-duality Jungmin Kim (Seoul National University) January 28, 2015 Talk based on [JK., Seok Kim, Kimyeong Lee] in progress. 6d N=(1,1) Little strings Outline NS5-branes in IIB string
More informationSupersymmetric Gauge Theories, Matrix Models and Geometric Transitions
Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions Frank FERRARI Université Libre de Bruxelles and International Solvay Institutes XVth Oporto meeting on Geometry, Topology and Physics:
More informationCurrent Algebra Constraints on Supersymmetric Quantum Field Theories
Current Algebra Constraints on Supersymmetric Quantum Field Theories Thomas Dumitrescu Harvard University arxiv:1602.01217, 1608.xxxxx with C. Córdova, K. Intriligator and work in progress with C. Córdova
More informationInstantons and Donaldson invariants
Instantons and Donaldson invariants George Korpas Trinity College Dublin IFT, November 20, 2015 A problem in mathematics A problem in mathematics Important probem: classify d-manifolds up to diffeomorphisms.
More informationTopological String Theory
Topological String Theory Hirosi Ooguri (Caltech) Strings 2005, Toronto, Canada If String Theory is an answer, what is the question? What is String Theory? If Topological String Theory is an answer, what
More informationModuli of heterotic G2 compactifications
Moduli of heterotic G2 compactifications Magdalena Larfors Uppsala University Women at the Intersection of Mathematics and High Energy Physics MITP 7.3.2017 X. de la Ossa, ML, E. Svanes (1607.03473 & work
More informationBPS Dyons, Wall Crossing and Borcherds Algebra
Simons Workshop on Geometry and Physics, 2008 BPS Dyons, Wall Crossing and Borcherds Algebra Erik Verlinde University of Amsterdam Based on work with Miranda Cheng Outline N=4 Dyonic Black Holes and Walls
More informationNUMBER THEORY IN STRING THEORY: SKEW, MOCK, FALSE, AND QUANTUM
NUMBER THEORY IN STRING THEORY: SKEW, MOCK, FALSE, AND QUANTUM Sarah M. Harrison based on work with Cheng, Duncan, Harvey, Kachru, Rayhaun ( 17) and Cheng, Chun, Ferrari, Gukov (to appear) INTRODUCTION
More informationarxiv: v2 [hep-th] 11 Oct 2009
RUNHETC-2008-11 Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions Wu-yen Chuang and Daniel Louis Jafferis NHETC, Department of Physics, Rutgers University arxiv:0810.5072v2
More informationDualities and 5-Brane Webs for 5d rank 2 SCFTs
Dualities and 5-Brane Webs for 5d rank 2 SCFTs Kimyeong Lee Korea Institute for Advanced Study Hirotaka Hayashi (Tokai Univ), Sung-Soo Kim (UESTC), Futoshi Yagi (Technion) [arxiv:1801.03916] and [arxiv:1806.10569]
More informationNon-Supersymmetric Seiberg duality Beyond the Planar Limit
Non-Supersymmetric Seiberg duality Beyond the Planar Limit Input from non-critical string theory, IAP Large N@Swansea, July 2009 A. Armoni, D.I., G. Moraitis and V. Niarchos, arxiv:0801.0762 Introduction
More informationKnots and Mirror Symmetry. Mina Aganagic UC Berkeley
Knots and Mirror Symmetry Mina Aganagic UC Berkeley 1 Quantum physics has played a central role in answering the basic question in knot theory: When are two knots distinct? 2 Witten explained in 88, that
More information4d N=2 as 6d N=(2,0) compactified on C
Yesterday Basics of 6d N=(2,0) theory. S-duality of 4d N=4. Today 4d N=2 as 6d N=(2,0) compactified on C Tomorrow Relation with 2d CFT Yesterday s talk s summary 6d N=(2,0) theory comes in types G= A,D,E
More informationMaximally Supersymmetric Solutions in Supergravity
Maximally Supersymmetric Solutions in Supergravity Severin Lüst Universität Hamburg arxiv:1506.08040, 1607.08249, and in progress in collaboration with J. Louis November 24, 2016 1 / 17 Introduction Supersymmetric
More informationBPS non-local operators in AdS/CFT correspondence. Satoshi Yamaguchi (Seoul National University) E. Koh, SY, arxiv: to appear in JHEP
BPS non-local operators in AdS/CFT correspondence Satoshi Yamaguchi (Seoul National University) E. Koh, SY, arxiv:0812.1420 to appear in JHEP Introduction Non-local operators in quantum field theories
More informationTopological reduction of supersymmetric gauge theories and S-duality
Topological reduction of supersymmetric gauge theories and S-duality Anton Kapustin California Institute of Technology Topological reduction of supersymmetric gauge theories and S-duality p. 1/2 Outline
More informationHilbert Series and Its Applications to SUSY Gauge Theories
Hilbert Series and Its Applications to SUSY Gauge Theories NOPPADOL MEKAREEYA Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) Progress in Quantum Field Theory and String Theory April 2012 Noppadol
More informationTopological Strings and Donaldson-Thomas invariants
Topological Strings and Donaldson-Thomas invariants University of Patras Πανɛπιστήµιo Πατρών RTN07 Valencia - Short Presentation work in progress with A. Sinkovics and R.J. Szabo Topological Strings on
More informationCalabi-Yau Fourfolds with non-trivial Three-Form Cohomology
Calabi-Yau Fourfolds with non-trivial Three-Form Cohomology Sebastian Greiner arxiv: 1512.04859, 1702.03217 (T. Grimm, SG) Max-Planck-Institut für Physik and ITP Utrecht String Pheno 2017 Sebastian Greiner
More informationAlgebraic structure of the IR limit of massive d=2 N=(2,2) theories. collaboration with Davide Gaiotto & Edward Witten
Algebraic structure of the IR limit of massive d=2 N=(2,2) theories IAS, October 13, 2014 Gregory Moore, Rutgers University collaboration with Davide Gaiotto & Edward Witten draft is ``nearly finished
More informationRefined Chern-Simons Theory, Topological Strings and Knot Homology
Refined Chern-Simons Theory, Topological Strings and Knot Homology Based on work with Shamil Shakirov, and followup work with Kevin Scheaffer arxiv: 1105.5117 arxiv: 1202.4456 Chern-Simons theory played
More informationA Localization Computation in Confining Phase
A Localization Computation in Confining Phase Seiji Terashima (YITP) 20 January 2015 at Osaka based on the paper: arxiv:1410.3630 Introduction 2 Analytic computations in QFT are hopeless, but, some exceptions:
More informationarxiv: v1 [hep-th] 4 Oct 2010 Walter Van Herck
Preprint typeset in JHEP style - HYPER VERSION KUL-TF-10/05 Exact indices for D particles, flow trees and the derived category arxiv:1010.0686v1 [hep-th] 4 Oct 2010 Walter Van Herck Institute for Theoretical
More informationFour Lectures on Web Formalism and Categorical Wall-Crossing. collaboration with Davide Gaiotto & Edward Witten
Four Lectures on Web Formalism and Categorical Wall-Crossing Lyon, September 3-5, 2014 Gregory Moore, Rutgers University collaboration with Davide Gaiotto & Edward Witten draft is ``nearly finished Plan
More informationF-theory and the classification of elliptic Calabi-Yau manifolds
F-theory and the classification of elliptic Calabi-Yau manifolds FRG Workshop: Recent progress in string theory and mirror symmetry March 6-7, 2015 Washington (Wati) Taylor, MIT Based in part on arxiv:
More informationBPS states in Matrix Strings
hep th/9704030 PUPT-694 BPS states in Matrix Strings Rajesh Gopakumar Department of Physics Princeton University Princeton, NJ 08544, USA Matrix string theory (or more generally U-Duality) requires Super
More informationString theory effects on 5D black strings
String theory effects on 5D black strings Alejandra Castro University of Michigan Work in collaboration with J. Davis, P. Kraus and F. Larsen hep-th/0702072, hep-th/0703087, 0705.1847[hep-th], 0801.1863
More informationDynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory
hep-th/9707042 MRI-PHY/P970716 Dynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory Ashoke Sen 1 2 Mehta Research Institute of Mathematics and Mathematical Physics Chhatnag Road, Jhusi,
More informationarxiv: v1 [hep-th] 23 Oct 2008
Preprint typeset in JHEP style - HYPER VERSION KUL-TF-08/25 The elliptic genus from split flows and Donaldson-Thomas invariants arxiv:0810.4301v1 [hep-th] 23 Oct 2008 Andrés Collinucci 1 and Thomas Wyder
More informationFunctional determinants, Index theorems, and Exact quantum black hole entropy
Functional determinants, Index theorems, and Exact quantum black hole entropy Sameer Murthy King s College London Strings 2015 Bengaluru, June 25, 2015 BPS black hole entropy is a detailed probe of aspects
More informationPredictions from F-theory GUTs. (High vs. low-scale SUSY; proton decay)
Predictions from F-theory GUTs Arthur Hebecker (Heidelberg) (including some original work with James Unwin (Notre Dame)) Outline: Motivation (Why F-theory GUTs?) Proton decay Flavor; neutrino masses Gauge
More informationExact Solutions of 2d Supersymmetric gauge theories
Exact Solutions of 2d Supersymmetric gauge theories Abhijit Gadde, IAS w. Sergei Gukov and Pavel Putrov UV to IR Physics at long distances can be strikingly different from the physics at short distances
More informationString Theory Compactifications with Background Fluxes
String Theory Compactifications with Background Fluxes Mariana Graña Service de Physique Th Journées Physique et Math ématique IHES -- Novembre 2005 Motivation One of the most important unanswered question
More informationDeconstructing the BPS sector of (2,0) Theories
Deconstructing the BPS sector of (2,0) Theories Costis Papageorgakis Aspen, 6 th March 2017 w/ J. Hayling, E. Pomoni and D. Rodríguez-Gómez 1703.xxxxx Motivation Many years on still trying to understand
More informationWall Crossing and Quivers
Wall Crossing and Quivers ddd (KIAS,dddd) dd 2014d4d12d Base on: H. Kim, J. Park, ZLW and P. Yi, JHEP 1109 (2011) 079 S.-J. Lee, ZLW and P. Yi, JHEP 1207 (2012) 169 S.-J. Lee, ZLW and P. Yi, JHEP 1210
More informationFramed BPS States In Two And Four Dimensions. Gregory Moore. String Math, Paris, June 27, 2016
Framed BPS States In Two And Four Dimensions Gregory Moore String Math, Paris, June 27, 2016 1 Review Derivation Of KSWCF From Framed BPS States (with A. Neitzke & D. Gaiotto, 2010, ) 2 3 Web Formalism
More informationMicrostates of AdS black holes and supersymmetric localization
Microstates of AdS black holes and supersymmetric localization Seyed Morteza Hosseini Università di Milano-Bicocca IPM, Tehran, May 8-11, 2017 Recent Trends in String Theory and Related Topics in collaboration
More informationThree-Charge Black Holes and ¼ BPS States in Little String Theory
Three-Charge Black Holes and ¼ BPS States in Little String Theory SUNGJAY LEE KOREA INSTITUTE FOR ADVANCED STUDIES Joint work (JHEP 1512, 145) with Amit Giveon, Jeff Harvey, David Kutasov East Asia Joint
More informationTheory III: String Theory. presented by Dieter Lüst, MPI and LMU-München
Theory III: String Theory presented by Dieter Lüst, MPI and LMU-München The string theory group at MPI (started in 2004): The string theory group at MPI (started in 2004): Permanent members: R. Blumenhagen,
More informationA Supergravity Dual for 4d SCFT s Universal Sector
SUPERFIELDS European Research Council Perugia June 25th, 2010 Adv. Grant no. 226455 A Supergravity Dual for 4d SCFT s Universal Sector Gianguido Dall Agata D. Cassani, G.D., A. Faedo, arxiv:1003.4283 +
More informationHeterotic Geometry and Fluxes
Heterotic Geometry and Fluxes Li-Sheng Tseng Abstract. We begin by discussing the question, What is string geometry? We then proceed to discuss six-dimensional compactification geometry in heterotic string
More information* +, ...! Einstein. [1] Calabi-Yau [2] Calabi-Yau. :;æåø!! :; õ ø!!
!"#$%$%&! '()*+,-./01+,-.234!!"#$%&'()! * +, -! 56789:;?@ABC
More informationBranes in Flux Backgrounds and Dualities
Workshop on recent developments in string effective actions and D-instantons Max-Planck-Institute fur Physik, Munich Branes in Flux Backgrounds and Dualities Giovanni Villadoro Harvard University based
More informationDisk Instantons, Mirror Symmetry and the Duality Web
HUTP-01/A023 HU-EP-01/21 hep-th/0105045 Disk Instantons, Mirror Symmetry and the Duality Web Mina Aganagic 1, Albrecht Klemm 2 and Cumrun Vafa 1 1 Jefferson Physical Laboratory Harvard University, Cambridge,
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationRigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1
Rigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1 Ofer Aharony Weizmann Institute of Science 8 th Crete Regional Meeting on String Theory, Nafplion, July 9, 2015 OA, Berkooz, Rey, 1501.02904 Outline
More informationPossible Advanced Topics Course
Preprint typeset in JHEP style - HYPER VERSION Possible Advanced Topics Course Gregory W. Moore Abstract: Potential List of Topics for an Advanced Topics version of Physics 695, Fall 2013 September 2,
More informationPhenomenological Aspects of LARGE Volume Models
Phenomenological Aspects of LARGE Volume Models Joseph P. Conlon (Cavendish Laboratory & DAMTP, Cambridge) 15th Irish Quantum Field Theory Meeting May(nooth) 2008 Phenomenological Aspects of LARGE Volume
More informationDEFECTS IN COHOMOLOGICAL GAUGE THEORY AND DONALDSON- THOMAS INVARIANTS
DEFECTS IN COHOMOLOGICAL GAUGE THEORY AND DONALDSON- THOMAS INVARIANTS SISSA - VBAC 2013 Michele Cirafici CAMGSD & LARSyS, IST, Lisbon CAMGSD @LARSyS based on arxiv: 1302.7297 OUTLINE Introduction Defects
More informationDirect generation of a Majorana mass for the Neutron from exotic instantons!
Direct generation of a Majorana mass for the Neutron from exotic instantons!? Andrea Addazi (Aquila, LNGS, INFN) Hot problems in particle physics, LNGS 2015 References 1) A. Addazi and M. Bianchi, arxiv:1407.2897
More informationAmoebas and Instantons
Joint Meeting of Pacific Region Particle Physics Communities (2006, 10/29-11/03, Waikiki) Amoebas and Instantons Toshio Nakatsu Talk based on Takashi Maeda and T.N., Amoebas and Instantons, hep-th/0601233.
More informationChern-Simons Theory & Topological Strings
1 Chern-Simons Theory & Topological Strings Bonn August 6, 2009 Albrecht Klemm 2 Topological String Theory on Calabi-Yau manifolds A-model & Integrality Conjectures B-model Mirror Duality & Large N-Duality
More informationDisk Instantons, Mirror Symmetry and the Duality Web
Disk Instantons, Mirror Symmetry and the Duality Web Mina Aganagic, Albrecht Klemm a, and Cumrun Vafa Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA a Institut für Physik,
More informationNew Toric Swiss Cheese Solutions
String Phenomenology 2017 (Based on arxiv:1706.09070 [hep-th]) Northeastern University 1/31 Outline Motivation 1 Motivation 2 CY Geometry Large Volume Scenario 3 Explicit Toric 4 2/31 Abundance of Moduli
More informationSpectral networks at marginal stability, BPS quivers, and a new construction of wall-crossing invariants
Spectral networks at marginal stability, BPS quivers, and a new construction of wall-crossing invariants Pietro Longhi Uppsala University String-Math 2017 In collaboration with: Maxime Gabella, Chan Y.
More information