Transcript Understanding the mechanism for the spontaneous breakdown

Putting M theory on computer
Jun Nishimura
KEK & Graduate University for
Advanced Studies (SOKENDAI)
Talk at LATTICE2007, Regensburg, July 31, 2007
based on collaboration with
Konstantinos Anagnostopoulos
(National Technical University, Athens)
Masanori Hanada
(RIKEN)
Shingo Takeuchi
(SOKENDAI)
Ref: Hanada-J.N.-Takeuchi, arXiv:0706.1647 [hep-lat]
Anagnostopoulos-Hanada- J.N.-Takeuchi, arXiv:0707.4454 [hep-th]
0. Introduction
large N gauge theories
playing more and more important roles in string/M theory
- non-pert. formulation of superstring/M theories
e.g.) Matrix Theory (Banks-Fischler-Shenker-Susskind ’97)
IIB matrix model (Ishibashi-Kawai-Kitazawa-Tsuchiya ’97)
 dynamical origin of space-time dimensionality,
gauge group, matters, etc.
- gauge/gravity duality
e.g.) AdS/CFT
Maldacena(’97)
 quantum description of black holes etc.
SUPERSYMMETRY on the lattice…
SUSY matrix quantum mechanics
1 dim. U(N) gauge theory with 16 supercharges
dimensional reduction
10d N=1 SYM
BFSS conjecture:
Banks-Fischler-Shenker-Susskind ’97
non-perturbative formulation of M theory
gauge/gravity correspondence (non-conformal ver.)
Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’98
finite T
dual geometry:
black D0 brane solution in type IIA SUGRA
Klebanov-Tseytlin ’96
Monte Carlo studies can
confirm the conjectured duality from first principles
Plan
0.
1.
2.
3.
4.
Introduction
SUSY matrix QM with 16 supercharges
non-lattice sim. for SUSY QM
Monte Carlo results
summary and discussions
1. SUSY matrix QM with 16 supercharges
Dim.Red.
pure SYM
10d
gauge field
1d gauge theory
Maj-Weyl
fermion
with adjoint matters
p.b.c.
anti p.b.c.

low T
strongly coupled
dual gravity description
high T
weakly coupled
high T exp.
(except for zero modes)
Kawahara-J.N.-Takeuchi
in prep.
2. Non-lattice simulation for SUSY QM
static diagonal gauge :
fixes sym. under
large gauge tr.
fixes the gauge inv. completely (specific to 1d)
Fourier mode expansion :
Advantages of the non-lattice simulation:
c.f.) lattice approach (Catterall’s talk)
 theoretically clean
Catterall-Wiseman, arXiv:0706.3518 [hep-lat]
the gauge-fixed action in the continuum except for
 restoration of SUSY (much faster than cont. lim.)
e.g.) in the 1d Wess-Zumino model
degenerate mass for boson and fermion
observed for
 cont. lim. approached faster than naïve expectation
from # of d.o.f..
higher modes : naturally suppressed by the kinetic term
 Fourier acceleration requires no extra cost.
removes critical slowing down completely
Catterall-Karamov ’02
compensates superficial increase in computational efforts
by factor of
3. Monte Carlo results
internal energy
free energy
high T exp.
(incl. next-leading)
obtained from
dual BH geometry
Polyakov line
high T exp.
(incl. next-leading)
characteristic behavior of
the deconfined phase
consistent with a speculation based
on gauge/gravity duality (Barbon et al., Aharony et al.)
c.f.) bosonic model (fermions omitted)
Kawahara-Takeuchi-J.N.
arXiv:0706.3517
high T exp. (leading only)
high T exp.
(incl. next-leading)
confined
deconfined
5. Summary and discussions
 the first Monte Carlo results for
matrix QM with maximal SUSY (16 supercharges)
plays important roles in superstring/M theory
non-lattice simulation method + Rational HMC method
Pfaffian
integrating out fermions
real positive to high accuracy
in the region of T investigated
no sign problem !
 high precision confirmation of gauge/gravity duality
from first principles
at small T
no phase transition (unlike the bosonic model)
Implications of our results
1) Microscopic d.o.f. which accounts for the B.H. entropy
has been identified.
c.f) much stronger results than
Strominger-Vafa (96)
2) SUSY gauge theory provides a natural framework
for quantum description of B.H.
at T not very small
(where classical description of B.H. is no more valid.)
For those who wish to gain some background…
Zwiebach, The first course in string theory
Becker-Becker-Schwartz, Superstring theory and M theory