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）　　　　　　　　　　

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 )

Ref : Hanada-Nishimura-S.T. arXiv:0706.1647[hep-lat] Anagnostopoulos-Hanada-Nishimura-S.T. arXiv:0707.4454[hep-th]

- BFSS matrix model and IIB matrix model

0. Introduction

non-pert. formulation of superstring/M theories

Large-N supersymmetric gauge theories

non-pert. study of superstring quantum description of BH

- AdS/CFT and gauge/gravity duality

Banks-Fischler-Shenker-Susskind ’97 Ishibashi-Kawai-Kitazawa-Tsuchiya ’97

Maldacena ’97Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’98

1 dim. U(N) gauge theory with 16 supercharges

- BFSS matrix model

N black D0 branes sol. in type IIA SUGRAlow T

(SUSY matrix quantum mechanics)

10d N=1 SYM

Dim. Red.

- gauge/gravity duality

non-pert. study of superstring/M theories

Monte Carlo simulation (first principle study)

strongly coupled

Large-N limit

c.f.) Kabat-Lfschytz-Lowe ’01 Kawahara-Nishimura-S.T. in prep.

Plan

0. Introduction

1. SUSY matrix QM with 16 supercharges

4. Summary and outlook

3-1. Monte Carlo results --- Energy

3-2. Monte Carlo results --- Polyakov line

2. Non-lattice simulation for SUSY QM

1. SUSY matrix QM with 16 supercharges

low T strongly coupled

high T weakly coupled

dual gravity

high T exp.Kawahara-Nishimura-S.T. in prep.

MW fermion

: temperature

: effective coupling constant

10d N=1 SYM

Dim. Red.

compactified

bosonic fields : p.b.c.

fermionic fields : anti p.b.c.

2. Non-lattice simulation for 1d SUSY QM

no need to use lattice

fixes the gauge sym. completely (specific to 1d)

Fourier mode cutoff

no need to use lattice

static diagonal gauge :

the importance of lattice lies in its gauge inv.

Advantages of the non-lattice simulation

theoretically clean

restoration of SUSY (faster than lattice)

convergence to cont. lim. (faster than lattice)

the gauge-fixed action in the continuum except for a cutoff

1d WZ model

〇 ◇ : non-lattice(our results)

△ ▽ : lattice (Giedt et al)

□ : lattice with half-SUSY (Catterall-Gregory)

(8)

(16)

3. Monte Carlo results of energy

high T exp.

from the dualtiy

gauge/gravity duality

Predicted behavior sets in at T = 0.5

(strongly coupled)

from the dualtiy

deconfined phase

high T exp.

Monte Carlo results of Polyakov line

(Barbon et al., Aharony et al.)

no phase transition gauge/gravity duality

confirmation of gauge/gravity duality in lower temp.

confirmation of gauge/string duality

5. Summary and outlook

evidences of gauge/gravity duality from first principles

non-lattice simulation method

no phase transition

low temp.

the first Monte Carlo results for 　 　

(strong coupling region)

c.f.) Strominger-Vafa ’96

quantum behavior of BH

outlook

the matrix QM with 16 supercharges

microscopic d.o.f. 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)

deconfined phase

confined phase