0 Introduction LargeN supersymmetric gauge theories BFSS matrix

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 - Ad. S/CFT and gauge/gravity duality Maldacena ’ 97 Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’ 98 non-pert. study of superstring quantum description of BH

10 d 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 Large-N limit low T strongly coupled c. f. ) Kabat-Lfschytz-Lowe ’ 01 Kawahara-Nishimura-S. T. in prep. N black D 0 branes sol. in type IIA SUGRA

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 10 d 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 high T strongly coupled dual gravity weakly coupled high T exp. Kawahara-Nishimura-S. T. in prep.

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

Advantages of the non-lattice simulation l theoretically clean the gauge-fixed action in the continuum except for a cutoff l restoration of SUSY (faster than lattice) l convergence to cont. lim. (faster than lattice) 1 d WZ model 〇◇: -lattice(our results) non △▽: lattice (Giedt et al) □: with half-SUSY Gregory) lattice (Catterall-(16) (8)

3. Monte Carlo results of energy from the dualtiy high T exp. from the dualtiy Predicted behavior sets in at T = 0. 5 (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. )

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

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

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