152 research outputs found
Little String Theory from Double-Scaling Limits of Field Theories
We show that little string theory on S^5 can be obtained as double-scaling
limits of the maximally supersymmetric Yang-Mills theories on RxS^2 and
RxS^3/Z_k. By matching the gauge theory parameters with those in the gravity
duals found by Lin and Maldacena, we determine the limits in the gauge theories
that correspond to decoupling of NS5-brane degrees of freedom. We find that for
the theory on RxS^2, the 't Hooft coupling must be scaled like ln^3(N), and on
RxS^3/Z_k, like ln^2(N). Accordingly, taking these limits in these field
theories gives Lagrangian definitions of little string theory on S^5.Comment: 16 pages, 5 figures. Minor change
First Results from Lattice Simulation of the PWMM
We present results of lattice simulations of the Plane Wave Matrix Model
(PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a
well-defined canonical ensemble. We simulate this theory by applying rational
hybrid Monte Carlo techniques to a naive lattice action. We examine the strong
coupling behaviour of the model focussing on the deconfinement transition.Comment: v3 20 pages, 8 figures, comment adde
Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
Recently a novel large-N reduction has been proposed as a maximally
supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the
planar limit. This proposal, if it works, will enable us to study the theory
non-perturbatively on a computer, and hence to test the AdS/CFT correspondence
analogously to the recent works on the D0-brane system. We provide a nontrivial
check of this proposal by performing explicit calculations in the large-N
reduced model, which is nothing but the so-called plane wave matrix model,
around a particular stable vacuum corresponding to RxS^3. At finite temperature
and at weak coupling, we reproduce precisely the deconfinement phase transition
in the N=4 super Yang-Mills theory on RxS^3. This phase transition is
considered to continue to the strongly coupled regime, where it corresponds to
the Hawking-Page transition on the AdS side. We also perform calculations
around other stable vacua, and reproduce the phase transition in super
Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and
RxS^2.Comment: 24 pages, 4 figure
Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski
signature (-+++). The condition of SO(4)-invariance imposed on gauge fields
yields a bosonic matrix model which is a consistent truncation of the plane
wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills
equations are reduced to the equation of a particle moving in the double-well
potential. The classical solution is a bounce, i.e. a particle which begins at
the saddle point \phi=0 of the potential, bounces off the potential wall and
returns to \phi=0. The gauge field tensor components parametrized by \phi are
smooth and for finite time both electric and magnetic fields are nonvanishing.
The energy density of this non-Abelian dyon configuration does not depend on
coordinates of R^1\times S^3 and the total energy is proportional to the
inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N)
Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy
is proportional to the square of the inverse radius of S^2. From the viewpoint
of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian
(dyonic) flux tubes extended along the x^3-axis.Comment: 11 pages; v2: one formula added, some coefficients correcte
Boundary operators in minimal Liouville gravity and matrix models
We interpret the matrix boundaries of the one matrix model (1MM) recently
constructed by two of the authors as an outcome of a relation among FZZT
branes. In the double scaling limit, the 1MM is described by the (2,2p+1)
minimal Liouville gravity. These matrix operators are shown to create a
boundary with matter boundary conditions given by the Cardy states. We also
demonstrate a recursion relation among the matrix disc correlator with two
different boundaries. This construction is then extended to the two matrix
model and the disc correlator with two boundaries is compared with the
Liouville boundary two point functions. In addition, the realization within the
matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page
Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have
sign problem in the continuum limit, that is, under the phase-quenched
simulation phase of the determinant localizes to 1 and hence the phase-quench
approximation becomes exact. Among several formulations, we study models by
Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem
is absent in both models and that they converge to the identical continuum
limit without fine tuning. We provide a simple explanation why previous works
by other authors, which claim an existence of the sign problem, do not capture
the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures
on U(1) mass independence and references added, to appear in JHE
N=4 SYM on R x S^3 and Theories with 16 Supercharges
We study N=4 SYM on R x S^3 and theories with 16 supercharges arising as its
consistent truncations. These theories include the plane wave matrix model, N=4
SYM on R x S^2 and N=4 SYM on R x S^3/Z_k, and their gravity duals were studied
by Lin and Maldacena. We make a harmonic expansion of the original N=4 SYM on R
x S^3 and obtain each of the truncated theories by keeping a part of the
Kaluza-Klein modes. This enables us to analyze all the theories in a unified
way. We explicitly construct some nontrivial vacua of N=4 SYM on R x S^2. We
perform 1-loop analysis of the original and truncated theories. In particular,
we examine states regarded as the integrable SO(6) spin chain and a
time-dependent BPS solution, which is considered to correspond to the AdS giant
graviton in the original theory.Comment: 68 pages, 12 figures, v2,v3:typos corrected and comments added. To
appear in JHE
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
We report on the results of numerical simulations of 1+1 dimensional SU(N)
Yang-Mills theory with maximal supersymmetry at finite temperature and
compactified on a circle. For large N this system is thought to provide a dual
description of the decoupling limit of N coincident D1-branes on a circle. It
has been proposed that at large N there is a phase transition at strong
coupling related to the Gregory-Laflamme (GL) phase transition in the
holographic gravity dual. In a high temperature limit there was argued to be a
deconfinement transition associated to the spatial Polyakov loop, and it has
been proposed that this is the continuation of the strong coupling GL
transition. Investigating the theory on the lattice for SU(3) and SU(4) and
studying the time and space Polyakov loops we find evidence supporting this. In
particular at strong coupling we see the transition has the parametric
dependence on coupling predicted by gravity. We estimate the GL phase
transition temperature from the lattice data which, interestingly, is not yet
known directly in the gravity dual. Fine tuning in the lattice theory is
avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified
for clarity. v3: Normalisation of lattice coupling corrected by factor of two
resulting in change of estimate for c_cri
Comments on large-N volume independence
We study aspects of the large-N volume independence on R**3 x L**G, where
L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We
find the critical number of lattice sites above which the center-symmetry
analysis on L**G agrees with the one on the continuum S**1. For Wilson
parameter set to one and G>=2, the two analyses agree. One-loop radiative
corrections to Wilson-line masses are finite, reminiscent of the
UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories.
Even for theories with G=1, volume independence in QCD(adj) may be guaranteed
to work by tuning one low-energy effective field theory parameter. Within the
parameter space of the theory, at most three operators of the 3d effective
field theory exhibit one-loop UV-sensitivity. This opens the analytical
prospect to study 4d non-perturbative physics by using lower dimensional field
theories (d=3, in our example).Comment: 12 pages; added small clarifications, published versio
Model of M-theory with Eleven Matrices
We show that an action of a supermembrane in an eleven-dimensional spacetime
with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and
an invariant symmetric bilinear form under an approximation. Thus, the action
under the conditions is manifestly covariant under volume preserving
diffeomorphism even when the world-volume metric is flat. Next, we propose two
3-algebraic models of M-theory which are obtained as a second quantization of
an action that is equivalent to the supermembrane action under the
approximation. The second quantization is defined by replacing Nambu-Poisson
bracket with finite-dimensional 3-algebras' brackets. Our models include eleven
matrices corresponding to all the eleven space-time coordinates in M-theory
although they possess not SO(1,10) but SO(1,2) x SO(8) or SO(1,2) x SU(4) x
U(1) covariance. They possess N=1 space-time supersymmetry in eleven dimensions
that consists of 16 kinematical and 16 dynamical ones. We also show that the
SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit
is taken.Comment: 20 pages, references, a table and discussions added, typos correcte
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