超対称行列量子力学の数値シミュレーション に基づくゲージ／重力対応の検証 発表者 : 竹内 紳悟(総研大) 共同研究者 : 　　Konstantinos Anagnostopoulos （Natl. Tech. U. , Athens） 　　花田 政範（理研） 西村 淳（KEK 総研大） Ref : Hanada-Nishimura-S.T. arXiv:0706.1647[hep-lat] Anagnostopoulos-Hanada-Nishimura-S.T. arXiv:0707.4454[hep-th] 基研研究会 「弦理論と場の理論 --- 量子と時空の最前線」 2007/8/6(月)-8/10(金)

0. Introduction Large-N supersymmetric gauge theories - BFSS matrix model and IIB matrix model Banks-Fischler-Shenker-Susskind ’97 Ishibashi-Kawai-Kitazawa-Tsuchiya ’97 non-pert. formulation of superstring/M theories - AdS/CFT and gauge/gravity duality Maldacena ’97 Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’98 まずイントロですが、ここでは超弦理論におけるlarge-N の超対称なゲージ理論の重要性 について述べさせて頂きます。 超弦理論、M理論の非摂動論的定式化は、．．．によって与えられます。 non-pert. study of superstring quantum description of BH

(SUSY matrix quantum mechanics) 10d N=1 SYM Dim. Red. 1 dim. U(N) gauge theory with 16 supercharges (SUSY matrix quantum mechanics) Monte Carlo simulation (first principle study) - BFSS matrix model non-pert. study of superstring/M theories - gauge/gravity duality c.f.) Kabat-Lfschytz-Lowe ’01 Kawahara-Nishimura-S.T. in prep. Large-N limit N black D0 branes sol. in type IIA SUGRA low T strongly coupled

2. Non-lattice simulation for SUSY QM Plan 0. Introduction 1. SUSY matrix QM with 16 supercharges 2. Non-lattice simulation for SUSY QM 3-1. Monte Carlo results --- Energy 3-2. Monte Carlo results --- Polyakov line 4. Summary and outlook

1. SUSY matrix QM with 16 supercharges 10d N=1 SYM Dim. Red. compactified bosonic fields : p.b.c. fermionic fields : anti p.b.c. MW fermion : temperature : effective coupling constant low T strongly coupled dual gravity high T weakly coupled high T exp. Kawahara-Nishimura-S.T. in prep.

2. Non-lattice simulation for 1d SUSY QM no need to use lattice the importance of lattice lies in its gauge inv. fixes the gauge sym. completely (specific to 1d) static diagonal gauge : no need to use lattice Fourier mode cutoff

Advantages of the non-lattice simulation theoretically clean the gauge-fixed action in the continuum except for a cutoff restoration of SUSY (faster than lattice) convergence to cont. lim. (faster than lattice) 1d WZ model 〇 ◇ : non-lattice(our results) △ ▽ : lattice (Giedt et al) restoration of SUSY (much faster than lattice and cont. lim.) convergence of cont. lim. (much faster than lattice ) □ : lattice with half-SUSY (Catterall-Gregory) (16) (8) compensates superficial increase in computational efforts by factor higher modes are suppressed by the kinetic term

gauge/gravity duality 3. Monte Carlo results of energy from the dualtiy high T exp. from the dualtiy Predicted behavior sets in at T = 0.5 gauge/gravity duality (strongly coupled)

gauge/gravity duality Monte Carlo results of Polyakov line high T exp. deconfined phase no phase transition gauge/gravity duality (Barbon et al., Aharony et al.)

confirmation of gauge/string duality 5. Summary and outlook the first Monte Carlo results for 　 　 the matrix QM with 16 supercharges low temp. (strong coupling region) non-lattice simulation method evidences of gauge/gravity duality from first principles c.f.) Strominger-Vafa ’96 no phase transition outlook confirmation of gauge/gravity duality in lower temp. microscopic d.o.f. of BH confirmation of gauge/string duality quantum behavior of BH

c.f. ) Polyakov line (1d SYM with 4 supercharges) high T exp.

c.f. ) Polyakov line (results of lattice) high T exp. (incl. next-leading) confined phase deconfined phase