18 research outputs found
The nature of ZZ branes
In minimal non-critical string theory we show that the principal (r,s) ZZ
brane can be viewed as the basic (1,1) ZZ boundary state tensored with the
(r,s) Cardy boundary state. In this sense there exists only one ZZ boundary
state, the basic (1,1) boundary state.Comment: 10 pages, footnote adde
Shaken, but not stirred - Potts model coupled to quantum gravity
We investigate the critical behaviour of both matter and geometry of the
three-state Potts model coupled to two-dimensional Lorentzian quantum gravity
in the framework of causal dynamical triangulations. Contrary to what general
arguments of the effects of disorder suggest, we find strong numerical evidence
that the critical exponents of the matter are not changed under the influence
of quantum fluctuations in the geometry, compared to their values on fixed,
regular lattices. This lends further support to previous findings that quantum
gravity models based on causal dynamical triangulations are in many ways better
behaved than their Euclidean counterparts.Comment: 19 pages, 9 figure
Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
We re-examine the perturbative properties of four-dimensional non-commutative
QED by extending the pinch techniques to the theta-deformed case. The explicit
independence of the pinched gluon self-energy from gauge-fixing parameters, and
the absence of unphysical thresholds in the resummed propagators permits a
complete check of the optical theorem for the off-shell two-point function. The
known anomalous (tachyonic) dispersion relations are recovered within this
framework, as well as their improved version in the (softly broken) SUSY case.
These applications should be considered as a first step in constructing
gauge-invariant truncations of the Schwinger-Dyson equations in the
non-commutative case. An interesting result of our formalism appears when
considering the theory in two dimensions: we observe a finite gauge-invariant
contribution to the photon mass because of a novel incarnation of IR/UV mixing,
which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde
Probability distribution of the index in gauge theory on 2d non-commutative geometry
We investigate the effects of non-commutative geometry on the topological
aspects of gauge theory using a non-perturbative formulation based on the
twisted reduced model. The configuration space is decomposed into topological
sectors labeled by the index nu of the overlap Dirac operator satisfying the
Ginsparg-Wilson relation. We study the probability distribution of nu by Monte
Carlo simulation of the U(1) gauge theory on 2d non-commutative space with
periodic boundary conditions. In general the distribution is asymmetric under
nu -> -nu, reflecting the parity violation due to non-commutative geometry. In
the continuum and infinite-volume limits, however, the distribution turns out
to be dominated by the topologically trivial sector. This conclusion is
consistent with the instanton calculus in the continuum theory. However, it is
in striking contrast to the known results in the commutative case obtained from
lattice simulation, where the distribution is Gaussian in a finite volume, but
the width diverges in the infinite-volume limit. We also calculate the average
action in each topological sector, and provide deeper understanding of the
observed phenomenon.Comment: 16 pages,10 figures, version appeared in JHE
Wilson line correlators in two-dimensional noncommutative Yang-Mills theory
We study the correlator of two parallel Wilson lines in two-dimensional
noncommutative Yang-Mills theory, following two different approaches. We first
consider a perturbative expansion in the large-N limit and resum all planar
diagrams. The second approach is non-perturbative: we exploit the Morita
equivalence, mapping the two open lines on the noncommutative torus (which
eventually gets decompacted) in two closed Wilson loops winding around the dual
commutative torus. Planarity allows us to single out a suitable region of the
variables involved, where a saddle-point approximation of the general Morita
expression for the correlator can be performed. In this region the correlator
nicely compares with the perturbative result, exhibiting an exponential
increase with respect to the momentum p.Comment: 21 pages, 1 figure, typeset in JHEP style; some formulas corrected in
Sect.3, one reference added, results unchange
Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model,
which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative
limit N -> infinity. The model can be used as a regularization of gauge theory
on noncommutative R^4_\theta in a particular scaling limit, which is studied in
detail. We also find topologically non-trivial U(1) solutions, which reduce to
the known "fluxon" solutions in the limit of R^4_\theta, reproducing their full
moduli space. Other solutions which can be interpreted as 2-dimensional branes
are also found. The quantization of the model is defined non-perturbatively in
terms of a path integral which is finite. A gauge-fixed BRST-invariant action
is given as well. Fermions in the fundamental representation of the gauge group
are included using a formulation based on SO(6), by defining a fuzzy Dirac
operator which reduces to the standard Dirac operator on S^2 x S^2 in the
commutative limit. The chirality operator and Weyl spinors are also introduced.Comment: 39 pages. V2-4: References added, typos fixe
Bogomolny equations for vortices in the noncommutative torus
We derive Bogomolny-type equations for the Abelian Higgs model defined on the
noncommutative torus and discuss its vortex like solutions. To this end, we
carefully analyze how periodic boundary conditions have to be handled in
noncommutative space and discussed how vortex solutions are constructed. We
also consider the extension to an model, a simplified
prototype of the noncommutative standard model.Comment: 23 pages, no figure
Asymptotic expansion of beta matrix models in the one-cut regime
We prove the existence of a 1/N expansion to all orders in beta matrix models
with a confining, off-critical potential corresponding to an equilibrium
measure with a connected support. Thus, the coefficients of the expansion can
be obtained recursively by the "topological recursion" of Chekhov and Eynard.
Our method relies on the combination of a priori bounds on the correlators and
the study of Schwinger-Dyson equations, thanks to the uses of classical complex
analysis techniques. These a priori bounds can be derived following Boutet de
Monvel, Pastur and Shcherbina, or for strictly convex potentials by using
concentration of measure. Doing so, we extend the strategy of Guionnet and
Maurel-Segala, from the hermitian models (beta = 2) and perturbative
potentials, to general beta models. The existence of the first correction in
1/N has been considered previously by Johansson and more recently by
Kriecherbauer and Shcherbina. Here, by taking similar hypotheses, we extend the
result to all orders in 1/N.Comment: 42 pages, 2 figures. v2: typos and a confusion of notation corrected.
v3: version to appear in Commun. Math. Phy
On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions
We present an investigation on the invariance properties of noncommutative
Yang-Mills theory in two dimensions under area preserving diffeomorphisms.
Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a
breaking of such an invariance, we confirm both on a fairly general ground and
by means of perturbative analytical and numerical calculations that indeed
invariance under area preserving diffeomorphisms is lost. However a remnant
survives, namely invariance under linear unimodular tranformations.Comment: LaTeX JHEP style, 16 pages, 2 figure
The Bethe Ansatz for Z_S Orbifolds of N=4 Super Yang-Mills Theory
Worldsheet techniques can be used to argue for the integrability of string
theory on AdS_5xS^5/Z_S, which is dual to the strongly coupled Z_S-orbifold of
N=4 SYM. We analyze the integrability of these field theories in the
perturbative regime and construct the relevant Bethe equations.Comment: 16 page