131 research outputs found
T-duality, Fiber Bundles and Matrices
We extend the T-duality for gauge theory to that on curved space described as
a nontrivial fiber bundle. We also present a new viewpoint concerning the
consistent truncation and the T-duality for gauge theory and discuss the
relation between the vacua on the total space and on the base space. As
examples, we consider S^3(/Z_k), S^5(/Z_k) and the Heisenberg nilmanifold.Comment: 24 pages, typos correcte
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
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
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
Multi-matrix models and emergent geometry
Encouraged by the AdS/CFT correspondence, we study emergent local geometry in
large N multi-matrix models from the perspective of a strong coupling
expansion. By considering various solvable interacting models we show how the
emergence or non-emergence of local geometry at strong coupling is captured by
observables that effectively measure the mass of off-diagonal excitations about
a semiclassical eigenvalue background. We find emergent geometry at strong
coupling in models where a mass term regulates an infrared divergence. We also
show that our notion of emergent geometry can be usefully applied to fuzzy
spheres. Although most of our results are analytic, we have found numerical
input valuable in guiding and checking our results.Comment: 1+34 pages, 4 figures. References adde
Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
We provide the geometrical meaning of the superconformal index.
With this interpretation, the superconformal index can be realized
as the partition function on a Scherk-Schwarz deformed background. We apply the
localization method in TQFT to compute the deformed partition function since
the deformed action can be written as a -exact form. The
critical points of the deformed action turn out to be the space of flat
connections which are, in fact, zero modes of the gauge field. The one-loop
evaluation over the space of flat connections reduces to the matrix integral by
which the superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major
revision, conclusions essentially unchanged, v5 published versio
Anatomy of bubbling solutions
We present a comprehensive analysis of holography for the bubbling solutions
of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring
of a 2-plane, which was argued to correspond to the phase space of free
fermions. We show that in general this phase space distribution does not
determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is
dual to, but it does determine it enough so that vevs of all single trace 1/2
BPS operators in that state are uniquely determined to leading order in the
large N limit. These are precisely the vevs encoded in the asymptotics of the
LLM solutions. We extract these vevs for operators up to dimension 4 using
holographic renormalization and KK holography and show exact agreement with the
field theory expressions.Comment: 67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded
explanations, more typos correcte
Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
In order to understand thermodynamical properties of N D-branes with chemical
potentials associated with R-symmetry charges, we study a one dimensional large
N gauge theory (bosonic BFSS type model) as a first step. This model is
obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills
theory and we use a 1/D expansion to investigate the phase structure. We find
three phases in the \mu-T plane. We also show that all the adjoint scalars
condense at large D and obtain a mass dynamically. This dynamical mass protects
our model from the usual perturbative instability of massless scalars in a
non-zero chemical potential. We find that the system is at least meta-stable
for arbitrary large values of the chemical potentials in D \to \infty limit. We
also explore the existence of similar condensation in higher dimensional gauge
theories in a high temperature limit. In 2 and 3 dimensions, the condensation
always happens as in one dimensional case. On the other hand, if the dimension
is higher than 4, there is a critical chemical potential and the condensation
happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3:
minor corrections, to appear in JHE
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