161 research outputs found
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
Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
We study theories with SU(2|4) symmetry, which include the plane wave matrix
model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess
many vacua. From Lin-Maldacena's method which gives the gravity dual of each
vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2
and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show
this directly on the gauge theory side. We clearly reveal relationships among
the spherical harmonics on S^3, the monopole harmonics and the harmonics on
fuzzy spheres. We extend the compactification (the T-duality) in matrix models
a la Taylor to that on spheres.Comment: 56 pages, 6 figures, v2:a footnote and references added, section 5.2
improved, typos corrected, v3:typos corrected, v4: some equations are
corrected, eq.(G.2) is added, conclusion is unchange
Coarse-Graining the Lin-Maldacena Geometries
The Lin-Maldacena geometries are nonsingular gravity duals to degenerate
vacuum states of a family of field theories with SU(2|4) supersymmetry. In this
note, we show that at large N, where the number of vacuum states is large,
there is a natural `macroscopic' description of typical states, giving rise to
a set of coarse-grained geometries. For a given coarse-grained state, we can
associate an entropy related to the number of underlying microstates. We find a
simple formula for this entropy in terms of the data that specify the geometry.
We see that this entropy function is zero for the original microstate
geometries and maximized for a certain ``typical state'' geometry, which we
argue is the gravity dual to the zero-temperature limit of the thermal state of
the corresponding field theory. Finally, we note that the coarse-grained
geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references 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
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
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
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
- …