超対称行列量子力学の数値シミュレーション...
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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. 共同研究者 : Konstantinos Anagnostopoulos ( Natl. Tech. U. , Athens ) 花田 政範(理研) 西村 淳( KEK 総研大). 発表者 : 竹内 紳悟 ( 総研大 ). Ref : Hanada-Nishimura-S.T. arXiv:0706.1647[hep-lat] - PowerPoint PPT PresentationTRANSCRIPT
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