204 research outputs found
Large N reduction for Chern-Simons theory on S^3
We study a matrix model which is obtained by dimensional reduction of
Chern-Simon theory on S^3 to zero dimension. We find that expanded around a
particular background consisting of multiple fuzzy spheres, it reproduces the
original theory on S^3 in the planar limit. This is viewed as a new type of the
large N reduction generalized to curved space.Comment: 4 pages, 2 figures, references added, typos correcte
Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
We study reduced matrix models obtained by the dimensional reduction of N=2
quiver Chern-Simons theories on S^3 to zero dimension and show that if a
reduced model is expanded around a particular multiple fuzzy sphere background,
it becomes equivalent to the original theory on S^3 in the large-N limit. This
is regarded as a novel large-N reduction on a curved space S^3. We perform the
localization method to the reduced model and compute the free energy and the
vacuum expectation value of a BPS Wilson loop operator. In the large-N limit,
we find an exact agreement between these results and those in the original
theory on S^3.Comment: 46 pages, 11 figures; minor modification
Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
Mass deformations of supersymmetric Yang-Mills theories in three spacetime
dimensions are considered. The gluons of the theories are made massive by the
inclusion of a non-local gauge and Poincare invariant mass term due to
Alexanian and Nair, while the matter fields are given standard Gaussian
mass-terms. It is shown that the dimensional reduction of such mass deformed
gauge theories defined on or produces matrix quantum
mechanics with massive spectra. In particular, all known massive matrix quantum
mechanical models obtained by the deformations of dimensional reductions of
minimal super Yang-Mills theories in diverse dimensions are shown also to arise
from the dimensional reductions of appropriate massive Yang-Mills theories in
three spacetime dimensions. Explicit formulae for the gauge theory actions are
provided.Comment: 20 Page
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
Large N reduction on group manifolds
We show that the large N reduction holds on group manifolds. Large N field
theories defined on group manifolds are equivalent to some corresponding matrix
models. For instance, gauge theories on S^3 can be regularized in a gauge
invariant and SO(4) invariant manner.Comment: 21 pages, 4 figures, typos corrected, a reference adde
Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM
Using the Eguchi-Kawai equivalence, we provide regularizations of
supersymmetric quiver and Chern-Simons gauge theories which leave the
supersymmetries unbroken. This allow us to study many interesting theories on a
computer. As examples we construct large- reduced models of supersymmetric
QCD with flavor and the ABJM model of multiple M2 branes.Comment: 21 pages, 2 figures, references 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
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
Decoupling limits of N=4 super Yang-Mills on R x S^3
We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with
gauge group SU(N). These decoupling limits lead to decoupled theories that are
much simpler than the full N=4 SYM but still contain many of its interesting
features. The decoupling limits correspond to being in a near-critical region,
near a point with zero temperature and critical chemical potentials. The new
decoupling limits are found by generalizing the limits of hep-th/0605234 to
include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM
but also the chemical potentials corresponding to the SO(4) symmetry. In the
decoupled theories it is possible to take a strong coupling limit in a
controllable manner since the full effective Hamiltonian is known. For planar
N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable
spin chains. We study the thermodynamics of the decoupled theories and find the
Hagedorn temperature for small and large values of the effective coupling. We
find an alternative formulation of the decoupling limits in the microcanonical
ensemble. This leads to a characterization of certain regimes of weakly coupled
N=4 SYM in which there are string-like states. Finally, we find a similar
decoupling limit for pure Yang-Mills theory, which for the planar limit leads
to a fully integrable decoupled theory.Comment: 48 pages, 1 figure; added references, published versio
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
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