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Talk at “Black Holes and Quantum Physics” workshop, Perimter Institute, Jan.24, ’09

Schwarzschild Radius and Black Hole Thermodynamics with Corrections from Simulations of SUSY Matrix Quantum Mechanics. Jun Nishimura (KEK). Talk at “Black Holes and Quantum Physics” workshop, Perimter Institute, Jan.24, ’09

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Talk at “Black Holes and Quantum Physics” workshop, Perimter Institute, Jan.24, ’09

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  1. Schwarzschild Radius and Black Hole Thermodynamics with Corrections from Simulations of SUSY Matrix Quantum Mechanics Jun Nishimura (KEK) Talk at “Black Holes and Quantum Physics” workshop, Perimter Institute, Jan.24, ’09 Ref.) Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 Hanada-Miwa-J.N.-Takeuchi, arXiv:0811.2081[hep-th] Hanada-Hyakutake-J.N.-Takeuchi,arXiv:0811.3102[hep-th]

  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) Schwarzschild radius and black hole...

  3. 0. Introduction

  4. Simulating Quantum Black Holes “quantum black hole” or microscopic description of black holes requires superstring theory CERN COURIER, March 2008 gauge/string duality (’98-) strongly coupled gauge theory Monte Carlo simulations analogous to lattice QCD • Anagnostopoulos-Hanada-J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454] Jun Nishimura (KEK) Schwarzschild radius and black hole...

  5. dim. U(N) ＳＹＭ curved 10d space-time low energy limit N A basis of gauge/gravity duality Maldacena (’97) • superstring massless modes open stringgauge particles,… closed stringgraviton, dilaton,… D brane“soliton solution” extending in -dim. (Direchlet) open string-closed string duality emission of a graviton propagation of a gauge particle Jun Nishimura (KEK) Schwarzschild radius and black hole...

  6. 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) Schwarzschild radius and black hole...

  7. Simulating superstrings inside a black hole black hole thermodynamics Anagnostopoulos-Hanada-J.N.-Takeuchi (’08) 7.41 Hanada-Hyakutake-J.N.-Takeuchi,arXiv:0811.3102 Schwarzschild radius from Wilson loop Hanada-Miwa-J.N.-Takeuchi, arXiv:0811.2081[hep-th] compatible with the fuzzball picture ! 1.89 Jun Nishimura (KEK) Schwarzschild radius and black hole...

  8. 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) Schwarzschild radius and black hole...

  9. Simulating SUSY QM with 16 supercharges

  10. 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) Schwarzschild radius and black hole...

  11. 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, PRD78 (08) 041502 Earlier works based on Gaussian approximation Kabat-Lifschytz-Lowe, PRL 86 (2001) 1426 Jun Nishimura (KEK) Schwarzschild radius and black hole...

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

  13. 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) Schwarzschild radius and black hole...

  14. 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) Schwarzschild radius and black hole...

  15. 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) Schwarzschild radius and black hole...

  16. 3. Higher derivative corrections to black hole thermodynamics from SUSY QM Hanada-Hyakutake-J.N.-Takeuchi, arXiv:0811.3102[hep-th]

  17. 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) Schwarzschild radius and black hole...

  18. Black hole thermodynamics with corrections curvature radius of the dual geometry More careful treatment leads to the same conclusion. (Hanada-Hyakutake-J.N.-Takeuchi,arXiv:0811.3102) Jun Nishimura (KEK) Schwarzschild radius and black hole...

  19. Higher derivative corrections toblack hole thermodynamics from SUSY QM Hanada-Hyakutake-J.N.-Takeuchi, arXiv:0811.3102[hep-th] higher derivative corrections slope = 4.6 finite cutoff effects Jun Nishimura (KEK) Schwarzschild radius and black hole...

  20. 3. Schwarzschild radius from Wilson loop Hanada-Miwa-J.N.-Takeuchi , arXiv:0811.2081[hep-th]

  21. Calculation of Wilson loop Hanada-Miwa-J.N.-Takeuchi, arXiv:0811.2081[hep-th] 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) Schwarzschild radius and black hole...

  22. 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) Schwarzschild radius and black hole...

  23. 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) Schwarzschild radius and black hole...

  24. Results: Wilson loop Hanada-Miwa-J.N.-Takeuchi, arXiv:0811.2081[hep-th] Schwarzschild radius from the Wilson loop high T exp. (next-leading) subleading term (perturbative corrections) Jun Nishimura (KEK) Schwarzschild radius and black hole...

  25. 5. Summary

  26. Summary and future prospects • 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) Schwarzschild radius and black hole...

  27. Simulating Quantum Universe Nonperturbative formulations of superstring/M theory Matrix Theory Type IIB matrix model Matrix String Theory Banks-Fischler-Shenker-Susskind (’97) Ishibashi-Kawai-Kitazawa-Tsuchiya (’97) Dijkgraaf-Verlinde-Verlinde (’97) How does our 4d space-time appear from 10d (11d) space-time ? e.g.) SO(10) SO(4) ? SSB 4Ｄ Gaussian expansion method J.N.-Sugino (’01), Kawai et al. (’01),... 10Ｄ Monte Carlo simulation, in progress Jun Nishimura (KEK) Schwarzschild radius and black hole...

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