ゲージ重力対応における バブリン グ の考え方 土屋麻人 静岡大学

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1 ゲージ重力対応における バブリン グ の考え方 土屋麻人 静岡大学

2 Introduction Candidates for nonperturbative definition of superstring ~ matrix model, large-n gauge theory Proposed models ~reduction of 10D SYM to lower dimensions 1. 0D IIB matrix model IKKT type IIB superstring 2. 1D Matrix theory BFSS M theory 3. 2D Matrix string theory DVV type IIA superstring 4. 4D SYM type IIB superstring on In 1 and 2, space-time is dynamically generated through distribution of matrix eigenvalues `emergence of space-time fluctuation of eingenvalue dist.~ particle talks by Kawai, Aoki, Umetsu, Nishimura and A similar interpretation for 4? Sugino is directly derived from SYM? This partially succeeds in bubbling AdS Lin-Lunin-Maldacena Maldacena

3 Contents Introduction Analogy with c=1 string Bubbling AdS Superstar Berenstein s model Conclusion and outlook

4 Analogy with c=1 string

5 matrix quantum mechanics (open string picture) 2D string with linear dilaton b.g. (closed string picture) open-closed duality : N free fermions Fermi surface Das-Jevicki Gross-Klebanov Polchinski Mcgreevy-Verlinde N-1 eigenvalue distribution ~ fermi surface fluctuation of eigenvalue distribution ~waves on fermi surface isolated eigenvalue Kuroki s talk one dimension closed string tacyon ZZ brane

6 (open string picture) (closed string picture) N=4 SYM ~theory on D3branes type IIB string on AdS5xS5 open-closed duality AdS5xS5 ~near horizon limit of D3-brane solution D3-brane in AdS5xS5 N-1 chiral primary states matrix model ~ free fermions eigenvalue distribution fluctuation of eigenvalue distribution ~waves on fermi surface isolated eigenvalue part of S5 KK graviton (AdS) giant graviton (D3-brane)

7 Bubbling AdS

8 Landau problem charged particle in magnetic field in 2D 2D harmonic oscillator angular momentum classical ground state (lowest Landau level) x2 x1

9 complex coordinate creation-annihilation operators eigenstates Lowest Landau level J=n holomorphic except for exponential factor

10 system of N fermions subtract the minimum momentum and rename it as J state with J=0 AdS5 x S5 from the total angular

11 classification of states with the total angular momentum J Young tableau specifies irreducible representations of GL(N,C) and SJ simultaneously Schur polynomial Kimura s talk Corley-Jevicki-Ramgoolam

12 giant graviton AdS giant graviton KK graviton

13 relation to phase space of 1D harmonic oscillator Wigner phase space distribution for 1D harmonic oscillator relation between charge density and WPSD in the classical limit Iso-Karabali-Sakita

14 Chiral primary operators and giant gravitons SYM on chiral primary operators of type half-bps extremal correlator non-renormalization theorem extremal correlators is independent of can be calculated using the free part Eden-Howe-Sokatchev-West propagator it

15 KK graviton with angular momentum J~O(1) giant graviton = D3-brane wrapped on S3 in S5 McGreevy-Suskind-Toumbas Balasubramanian-Berkooz-Naqvi-Strassler J~O(N) size R: radius of S5 AdS giant graviton = D3-brane wrapped on S3 in AdS5 Hashimoto-Hirano-Itzhaki Grisaru-Myers-Tafjord Corley-Jevicki-Ramgoolam J~O(N) no restriction on J KK graviton giant graviton dual giant

16 Orhogonal basis

17 SYM on global coordinates of AdS5 boundary relation between and conformally equiv. on operator on on state on

18 chiral primary states s-wave of KK decompositions only t-dependence preserve 16 susy R SO(4) SO(4) R-symmetry SO(6) free part of ~ complex matrix model kinetic term s-wave on S3 Hashimoto-Hirano-Itzhaki Corley-Jevicki-Ramgoolam Berenstein Takayama-A.T. coupling of conformal matter to curvature of S3

19 operator-state correspondence

20 giant graviton AdS giant graviton KK graviton

21 Bubbling AdS Lin-Lunin-Maldacena general form of half-bps sof type IIB sugra that preserve R SO(4) SO(4) isometry characterized by a single function z(x1,x2, y) differential eq. satisfied by z z must take ½ (white) or -½ (black) on the plane y=0 for the solution to be smooth configuration of droplet geometry

22 shrinking S3 y=0 topology of droplet (bubble) topology of space-time flux Area is quantized

23 example x2 r0 geometry AdS/CFT duality quantized! area of droplet x2 droplet and S5 r0 x1 x1

24 Identification with Fermi droplets quantization of area area of droplet~ flux area of droplet x2 enegy and angular momentum x1 total energy of N fermions ground state ground state energy x2 r0 x1 ground state of fermions

25 KK graviton and (AdS) giant graviton KK graviton with angular momentum J x2 ~KK graviton with angular x1 momentum J Grant-Maoz-Marsano-Papadodimas-Rychkov giant graviton with J O(N) AdS giant graviton with J O N x2 x2 x1 x1

26 Further developments General half-bps operators Yoneya Cuntz algebra+free fermions Bubbling Wilson loop Yamaguchi, Kuroki s talk IIA bubbling~ SU(2 4) symmetric solution of IIA sugra Lin-Maldacena Electrostatics in an axially symmetric system in 3D gravity duals of Vacua in SU(2 4) symmetric theories Relations between SU(2 4) symmetric theories Ishiki-Shimasaki-Takayma-Tsuchiya, Shimasaki s talk

27 Superstar

28 extremal limit of black hole with one charge in 5D N=2 gauged SUGRA lifted to ten dimensions Behrndt-Chamseddine-Sabra Superstar (ten-dimensional form) naked singularity at Behrndt-Cvetic-Sabra Cvetic et. al.

29 LLM geometry CTC regular region naked singularity chronology protection Caldarelli-Klemm-Silva Milanesi-O Loughlin Pauli exclusion principle

30 smooth geometry pure state superstar, hyperstar mixed states Ensemble of Young diagrams ~ limit shape entropy entropy? Balasubramanian-de Boer-Jejjala-Simon Buchel, Suryanarayana,,,,,,,,,,

31 Berenstein s model Berenstein, Berenstein-Correa-Vazquez, Berenstein-Vazquez, Berenstein-Cotta, Berenstein-Cotta-Leonardi

32 truncation keep only s-wave on S3 of six scalars and supersymmetric states excite only these modes in the free limit and supersymmetry should account for cancelations of quantum corrections integration over hamiltonian large t Hooft coupling Gauss law constraint

33 hamiltonian inner product wave function for ground state redefinition of wave function probability distribution for N particles cf.) d=2

34 N limit constraint saddle point approximation contradiction for for Confirmed by numerical simulation OK

35 hamiltonian for off-diagonal part BMN-type state energy

36 Giant magnon i i

37 Summary Emergent geometry in AdS/CFT Analogy with c=1 string Bubbling AdS ~ chiral primary states emergence of part of S5 chronology protection, mixed states Attempt for emergence of full S5 outlook emergence of AdS5xS5 thermodynamics 1/N correction (string correction) Implication for IIB matrix model

38 例1 pp wave geometry x2 x1