Physik Clean

Document Sample
Physik Clean Powered By Docstoc
					       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

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


                                                               pure SYM

1d gauge theory                                               gauge field
    with adjoint matters                                      fermion
                                         anti p.b.c.


        low T              strongly coupled   dual gravity description
        high T             weakly coupled       high T exp.
                      (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.

                               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

Shared By: