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

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
non-pert. study of superstring
quantum description of BH
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
Large-N limit
low T
strongly coupled
c.f.)
Kabat-Lfschytz-Lowe ’01
Kawahara-Nishimura-S.T. in prep.
N black D0 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
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
high T
strongly coupled
dual gravity
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)
□:
lattice with half-SUSY
(Catterall-Gregory)
(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
 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

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