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Putting M theory on computer

Putting M theory on computer. Talk at LATTICE2007 , Regensburg, July 31, 2007. Jun Nishimura KEK & Graduate University for Advanced Studies ( SOKENDAI ). based on collaboration with Konstantinos Anagnostopoulos (National Technical University, Athens)

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Putting M theory on computer

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  1. Putting M theory on computer Talk atLATTICE2007, Regensburg, July 31, 2007 Jun Nishimura KEK & Graduate University for Advanced Studies (SOKENDAI) based on collaboration with Konstantinos Anagnostopoulos (National Technical University, Athens) Masanori Hanada (RIKEN) Shingo Takeuchi (SOKENDAI) Ref: Hanada-J.N.-Takeuchi, arXiv:0706.1647 [hep-lat] Anagnostopoulos-Hanada- J.N.-Takeuchi, arXiv:0707.4454 [hep-th]

  2. 0. Introduction large N gauge theories playing more and more important roles in string/M theory - 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/gravity duality e.g.) AdS/CFT Maldacena(’97) • quantum description of black holes etc. SUPERSYMMETRY on the lattice…

  3. SUSY matrix quantum mechanics 1 dim. U(N) gauge theory with 16 supercharges dimensional reduction 10d N=1 SYM BFSS conjecture: Banks-Fischler-Shenker-Susskind ’97 non-perturbative formulation of M theory gauge/gravity correspondence (non-conformal ver.) Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’98 dual geometry: black D0 brane solution in type IIA SUGRA finite T Klebanov-Tseytlin ’96 Monte Carlo studies can confirm the conjectured duality fromfirst principles

  4. Plan 0. Introduction 1. SUSY matrix QM with 16 supercharges 2. non-lattice sim. for SUSY QM 3. Monte Carlo results 4. summary and discussions

  5. Dim.Red. pure SYM 10d gauge field Maj-Weyl fermion 1. SUSY matrix QM with 16 supercharges 1d gauge theory with adjoint matters p.b.c. anti p.b.c. low T strongly coupled dual gravity description high T weakly coupled high T exp. Kawahara-J.N.-Takeuchi in prep. (except for zero modes)

  6. 2. Non-lattice simulation for SUSY QM static diagonal gauge : fixes sym. under large gauge tr. fixes the gauge inv. completely (specific to 1d) Fourier mode expansion :

  7. Advantages of the non-lattice simulation: c.f.) lattice approach (Catterall’s talk) Catterall-Wiseman, arXiv:0706.3518 [hep-lat] • theoretically clean the gauge-fixed action in the continuum except for • restoration of SUSY (much faster than cont. lim.) e.g.) in the 1d Wess-Zumino model degenerate mass for boson and fermion observed for • cont. lim. approached faster than naïve expectation from # of d.o.f.. higher modes : naturally suppressed by the kinetic term • Fourier acceleration requires no extra cost. removes critical slowing down completely Catterall-Karamov ’02 compensates superficial increase in computational efforts by factor of

  8. 3. Monte Carlo results internal energy free energy high T exp. (incl. next-leading) obtained from dual BH geometry

  9. characteristic behavior of the deconfined phase Polyakov line high T exp. (incl. next-leading) consistent with a speculation based ongauge/gravity duality(Barbon et al., Aharony et al.)

  10. high T exp. (incl. next-leading) c.f.) bosonic model (fermions omitted) Kawahara-Takeuchi-J.N. arXiv:0706.3517 high T exp. (leading only) confined deconfined

  11. 5. Summary and discussions • the first Monte Carlo results for matrix QM with maximalSUSY (16 supercharges) plays important roles in superstring/M theory non-lattice simulation method + Rational HMC method Pfaffian integrating out fermions real positive to high accuracy in the region of T investigated no sign problem ! • high precision confirmation of gauge/gravity duality from first principles at small T no phase transition (unlike the bosonic model)

  12. Implications of our results • Microscopic d.o.f. which accounts for the B.H. entropy • has been identified. c.f) much stronger results than Strominger-Vafa (96) 2) SUSY gauge theory provides a natural framework for quantum description of B.H. at T not very small (where classical description of B.H. is no more valid.) For those who wish to gain some background… Zwiebach, The first course in string theory Becker-Becker-Schwartz, Superstring theory and M theory

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