1. 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: [hep-lat]
Anagnostopoulos-Hanada-Nishimura-S.T. arXiv: [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)

2. 0. Introduction Large-N supersymmetric gauge theories
- BFSS matrix model and IIB matrix model
Banks-Fischler-Shenker-Susskind ’ 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

3. (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 ’ Kawahara-Nishimura-S.T. in prep.
Large-N limit
N black D0 branes sol. in type IIA SUGRA
low T
strongly coupled

4. 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

5. 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.

6. 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

7. 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

8. 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)

9. 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.)

10. 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

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

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