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Simulating Superstrings inside a Black Hole

Simulating Superstrings inside a Black Hole. Jun Nishimura (KEK). Nov.1, ’08, RIKEN workshop “New Developments in Gauge Theory Driven by Numerical Simulation”. based on collaborations with Konstantinos Anagnostopoulos (National Technical University, Athens, Greece)

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Simulating Superstrings inside a Black Hole

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  1. Simulating Superstrings inside a Black Hole Jun Nishimura (KEK) Nov.1, ’08, RIKEN workshop “New Developments in Gauge Theory Driven by Numerical Simulation”

  2. based on collaborations with • Konstantinos Anagnostopoulos • (National Technical University, Athens, Greece) • Masanori Hanada (Weizmann Inst., Israel) • Yoshifumi Hyakutake (Osaka Univ.) • Akitsugu Miwa • (U. of Tokyo, Komaba • → Harish-Chandra Research Inst., India) • Shingo Takeuchi (KEK → APCTP, Korea) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  3. 0. Introduction

  4. Supersymmetric large-N gauge theories suitable formulation for describing superstrings non-perturbatively - non-pert. formulation of superstring/M theories e.g.) Matrix Theory (Banks-Fischler-Shenker-Susskind ’97) IIB matrix model (Ishibashi-Kawai-Kitazawa-Tsuchiya ’97) • dynamical origin of space-time dimensionality, gauge group, matters, etc. - gauge/string duality e.g.) AdS/CFT Maldacena (’97) • quantum/stringy description of black holes in terms of gauge theories Difficulty : Strongly coupled dynamics should be investigated ! Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  5. Monte Carlo simulation can be a powerful approach as in lattice QCD, but… (c.f., T.Onogi’s talk) SUSY : broken on the lattice translational symmetries broken to discrete ones • Lattice formulation preserving a part of supersymmetry • by using various ideas such as twisting, orbifolding, … (Kaplan,Unsal,Catterall,Sugino,Suzuki,Kanamori, Kawamoto,Nagata,Damgaard,Matsuura,…) (c.f., I.Kanamori’s talk) • Non-lattice approach respecting SUSY maximally systems with 16 supercharges can be studied ! (This talk) 1d gauge theory (SUSY matrix QM) non-perturbative gauge fixing + Fourier mode cutoff (c.f., A.Tsuchiya’s talk) fuzzy sphere Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  6. This talk Supersymmetric matrix quantum mechanics 1d U(N) gauge theory with 16 supercharges non-perturbative formulation of M theory BFSS conjecture Banks-Fischler-Shenker-Susskind (’97) low energy effective theory of N D0 branes gauge/gravity correspondence(non-conformal ver.) Itzhaki-Maldacena-Sonnenschein-Yankielowicz (’98) SUSY mass deformation plane-wave matrix model Berenstein-Maldacena-Nastase (’02) Expanding around a (multi-)fuzzy-sphere background Ishii-Ishiki-Shimasaki-Tsuchiya (’08) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  7. 1d U(N) SUSY gauge theory Gauge-gravity duality for D0-brane system type IIA superstring Itzhaki-Maldacena-Sonnenschein -Yankielowicz (’98) N D0 branes horizon t black 0-brane solution in type IIA SUGRA near-extremal black hole at finite T In the decoupling limit, the D0 brane system describes the black hole microscopically. SUGRA description : valid Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  8. Simulating superstrings inside a black hole black hole thermodynamics Anagnostopoulos-Hanada-J.N.-Takeuchi (’08) 7.41 Hanada-Hyakutake-J.N.-Takeuchi, in prep. Schwarzschild radius from Wilson loop Hanada-Miwa-J.N.-Takeuchi, in prep. 1.89 Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  9. Plan of the talk • 0. Introduction • 1. Simulating SUSY matrix QM with 16 supercharges • 2. Dual gravity description and black hole thermodynamics • 3. Higher derivative corrections to black hole thermodynamics • from SUSY QM • 4. Schwarzschild radius from Wilson loop • 5. Summary Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  10. Simulating SUSY QM with 16 supercharges

  11. SUSY matrix QM with 16 supercharges 1d gauge theory p.b.c. anti p.b.c. (without loss of generality) low T strongly coupled dual gravity description high T non-zero modes : weakly coupled (high T exp.) (zero modes : integrated non-perturbatively) Kawahara-J.N.-Takeuchi, JHEP 0712 (2007) 103, arXiv:0710.2188[hep-th] Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  12. should be fixed by imposing Fourier-mode simulationrespecting SUSY maximally Hanada-J.N.-Takeuchi, PRL 99 (07) 161602 [arXiv:0706.1647] Note: Gauge symmetry can be fixed non-perturbativelyin 1d. • static diagonal gauge : • residual gauge symmetry : c.f.) lattice approach : Catterall-Wiseman, arXiv:0803.4273[hep-th] Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  13. 2. Dual gravity descriptionand black hole thermodynamics Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454]

  14. Dual gravity description After taking the decoupling limit : range of validity: Black hole thermodynamics Hawking temperature : Bekenstein-Hawking entropy : Klebanov-Tseytlin (’96) 7.41 Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  15. Result: Internal energy Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454] free energy high T expansion (incl. next-leading order) result obtained from 10d BH Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  16. Result: Polyakov line Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454] High T expansion (including next-leading order) Characteristic behavior of the deconfined phase no phase transition unlike in bosonic case consistent with analyses on the gravity size (Barbon et al., Aharony et al.) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  17. 3. Higher derivative corrections to black hole thermodynamics from SUSY QM Hanada-Hyakutake-J.N.-Takeuchi, in prep.

  18. corrections to type IIA SUGRA action low energy effective action of type IIA superstring theory tree-level scattering amplitudes of the massless modes leading term : type IIA SUGRA action explicit calculations of 2-pt and 3-pt amplitudes 4-pt amplitudes Complete form is yet to be determined, but we can still make a dimensional analysis. Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  19. Black hole thermodynamics with corrections curvature radius of the dual geometry More careful treatment leads to the same conclusion. (Hanada-Hyakutake-J.N.-Takeuchi, in prep.) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  20. Higher derivative corrections toblack hole thermodynamics from SUSY QM higher derivative corrections slope = 4.6 finite cutoff effects (?) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  21. 3. Schwarzschild radius from Wilson loop Hanada-Miwa-J.N.-Takeuchi, in prep.

  22. Calculation of Wilson loop Hanada-Miwa-J.N.-Takeuchi, in prep. N D0 branes horizon Rey-Yee (’98), Maldacena (’98) probe D0 brane t fundamental string gauge theory side : propagation of a test particle coupled to Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  23. Calculation of Wilson loop (cont’d) horizon probe D0 brane Replace N D0 branes by the black 0-brane background fundamental string gravity theory side : string action for the minimal surface : propagation of the string in the b.g. geometry Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  24. Calculation of Wilson loop (cont’d) perimeter-law suppression factor due to propagation of a particle with mass M more sophisticated justification a la Drukker-Gross-Ooguri (’99) natural to identify 1.89 Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  25. Results: Wilson loop Schwarzschild radius from the Wilson loop high T exp. (next-leading) subleading term (perturbative corrections) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  26. 5. Summary

  27. Summary • Monte Carlo studies of supersymmetric large N gauge theories powerful method for superstring theory • simulating superstringsinside a black hole based on gauge/string duality • Black hole thermodynamics (E v.s. T relation) Schwarzschild radius reproduced from Wilson loop • a highlynontrivial check of the duality • microscopic origin of the black hole thermodynamics • including higher derivative corrections ! Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

  28. SO(6) SO(3) from Gaussian expansion (Aoyama-J.N.-Okubo, in prep.) Future prospects • extension to lower SUSY case (Hanada-Matsuura-J.N., in progress) easier, and many things to explore • higher dimensional case possible using mass deformation (Ishiki-Kim-J.N.-Tsuchiya, in progress) • so far, planar limit important next step is to study non-planar limit Matrix theory, IIB matrix model sign problem has to be treated carefully toy model(Anagnostopoulos-Azuma-J.N., in prep.) 6d IKKT model(Aoyama-Azuma-Hanada-J.N., in progress) Jun Nishimura (KEK) Simulating Superstrings inside a Black Hole

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