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					       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


                       dual geometry:
   finite T            black D0 brane solution in type IIA SUGRA
                                      Klebanov-Tseytlin ’96

  Monte Carlo studies can
  confirm the conjectured duality from first principles
                  Plan



0.   Introduction
1.   SUSY matrix QM with 16 supercharges
2.   non-lattice sim. for SUSY QM
3.   Monte Carlo results
4.   summary and discussions
    1. SUSY matrix QM with 16 supercharges

                                                       Dim.Red.

                                                               pure SYM

                                                              10d
1d gauge theory                                               gauge field
                                                              Maj-Weyl
    with adjoint matters                                      fermion
                                         p.b.c.
                                         anti p.b.c.



        low T              strongly coupled   dual gravity description
        high T             weakly coupled       high T exp.
                                                   Kawahara-J.N.-Takeuchi
                      (except for zero modes)
                                                   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)
                              Catterall-Wiseman, arXiv:0706.3518 [hep-lat]
  theoretically clean
     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
                                             no sign problem !
       in the region of T investigated

 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

				
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posted:12/9/2012
language:English
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