223 research outputs found
Towards an explicit expression of the Seiberg-Witten map at all orders
The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge
theories, and allows to express the noncommutative variables in terms of the
commutative ones. Its explicit form can be found order by order in the
noncommutative parameter theta and the gauge potential A by the requirement
that gauge orbits are mapped on gauge orbits. This of course leaves
ambiguities, corresponding to gauge transformations, and there is an infinity
of solutions. Is there one better, clearer than the others ? In the abelian
case, we were able to find a solution, linked by a gauge transformation to
already known formulas, which has the property of admitting a recursive
formulation, uncovering some pattern in the map. In the special case of a pure
gauge, both abelian and non-abelian, these expressions can be summed up, and
the transformation is expressed using the parametrisation in terms of the gauge
group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio
c=1 Matrix Models: Equivalences and Open-Closed String Duality
We give an explicit demonstration of the equivalence between the Normal
Matrix Model (NMM) of c=1 string theory at selfdual radius and the
Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic
loop expectation values in the NMM to condensates of the closed string tachyon,
and discuss the implications for open-closed duality. As in c<1, the
Kontsevich-Miwa transform between the parameters of the two theories appears to
encode open-closed string duality, though our results also exhibit some
interesting differences with the c<1 case. We also briefly comment on two
different ways in which the Kontsevich model originates.Comment: 27 pages, latex, 1 figure, typos, discussion added, acknowledgements
update
Noncritical String Correlators, Finite-N Matrix Models and the Vortex Condensate
We carry out a systematic study of correlation functions of momentum modes in
the Euclidean c=1 string, as a function of the radius and to all orders in
perturbation theory. We obtain simple explicit expressions for several classes
of correlators in terms of special functions. The Normal Matrix Model is found
to be a powerful calculational tool that computes c=1 string correlators even
at finite N. This enables us to obtain a simple combinatoric formula for the
2n-point function of unit momentum modes, which after T-duality determines the
vortex condensate. We comment on possible applications of our results to
T-duality at c=1 and to the 2d black hole/vortex condensate problem.Comment: 38 pages, LaTe
Kinematical Analogy for Marginal Dyon Decay
We describe a kinematical analogy for the marginal decay of 1/4-BPS dyons in
4-dimensional N=4 string compactifications. In this analogy, the electric and
magnetic charges play the role of spatial momenta, the BPS mass plays the role
of energy, and 1/2-BPS dyons correspond to massless particles. Using SO(12,1)
"Lorentz" invariance and standard kinematical formulae in particle physics, we
provide simple derivations of the curves of marginal stability. We also show
how these curves map into the momentum ellipsoid, and propose some applications
of this analogy.Comment: 10 pages, minor revision
Hodge Duality Operation And Its Physical Applications On Supermanifolds
An appropriate definition of the Hodge duality operation on any
arbitrary dimensional supermanifold has been a long-standing problem. We define
a working rule for the Hodge duality operation on the -dimensional supermanifold parametrized by a couple of even (bosonic)
spacetime variables and a couple of Grassmannian (odd)
variables and of the Grassmann algebra. The Minkowski
spacetime manifold, hidden in the supermanifold and parametrized by , is chosen to be a flat manifold on which a two -dimensional
(2D) free Abelian gauge theory, taken as a prototype field theoretical model,
is defined. We demonstrate the applications of the above definition (and its
further generalization) for the discussion of the (anti-)co-BRST symmetries
that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge
theories considered on the four - (and six )-dimensional
supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio
A new approach to the analysis of a noncommutative Chern-Simons theory
A novel approach to the analysis of a noncommutative Chern--Simons gauge
theory with matter coupled in the adjoint representation has been discussed.
The analysis is based on a recently proposed closed form Seiberg--Witten map
which is exact in the noncommutative parameter.Comment: 9 pages latex, some new results added. To be published in Modern
Physics Letters
Non-BPS Brane Cosmology
We study cosmology on a BPS D3-brane evolving in the 10D SUGRA background
describing a non-BPS brane. Initially the BPS brane is taken to be a probe
whose dynamics we determine in the non-compact non-BPS background. The
cosmology observed on the brane is of the FRW type with a scale factor
. In this mirage cosmology approach, there is no self-gravity on the
brane which cannot inflate. Self-gravity is then included by compactifying the
background space-time. The low energy effective theory below the
compactification scale is shown to be bi-metric, with matter coupling to a
different metric than the geometrically induced metric on the brane. The
geometrical scale factor on the brane is now where
arises from brane self-gravity. In this non-BPS scenario the brane generically
inflates. We study the resulting inflationary scenario taking into account the
fact that the non-BPS brane eventually decays on a time-scale much larger than
the typical inflationary time-scale. After the decay, the theory ceases to be
bi-metric and COBE normalization is used to estimate the string scale which is
found to be of order GeV.Comment: 20 pages, JHEP3.cl
Topological Chern-Simons Sigma Model
We consider topological twisting of recently constructed Chern-Simons-matter
theories in three dimensions with N=4 or higher supersymmetry. We enumerate
physically inequivalent twistings for each N, and find two different twistings
for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4
topological theories, which we call A/B-models, in full detail. The A-model has
been recently studied by Kapustin and Saulina. The B-model is new and it
consists solely of a Chern-Simons term of a complex gauge field up to
BRST-exact terms. We also compare the new theories with topological Yang-Mills
theories and find some interesting connections. In particular, the A-model
seems to offer a new perspective on Casson invariant and its relation to
Rozansky-Witten theory.Comment: 31 pages, no figure; v2. references adde
String Interactions in PP-Waves
We argue that string interactions in a PP-wave spacetime are governed by an
effective coupling g_{eff}=g_s(\mu p^+\apm)f(\mu p^+ \apm) where f(\mu p^+
\apm) is proportional to the light cone energy of the string states involved
in the interaction. This simply follows from generalities of a Matrix String
description of this background. nicely interpolates between the
expected result () for flat space (small \mu p^+\apm) and a recently
conjectured expression from the perturbative gauge theory side (large \mu
p^+\apm).Comment: 8 page
PP Wave Limit and Enhanced Supersymmetry in Gauge Theories
We observe that the pp wave limit of compactifications of
type IIB string theory is universal, and maximally supersymmetric, as long as
is smooth and preserves some supersymmetry. We investigate a specific
case, . The dual SCFT, describing D3-branes at a
conifold singularity, has operators that we identify with the oscillators of
the light-cone string in the universal pp-wave background. The correspondence
is remarkable in that it relies on the exact spectrum of anomalous dimensions
in this CFT, along with the existence of certain exceptional series of
operators whose dimensions are protected only in the limit of large `t Hooft
coupling. We also briefly examine the singular case , for which
the pp wave background becomes a orbifold of the maximally supersymmetric
background by reflection of 4 transverse coordinates. We find operators in the
corresponding SCFT with the right properties to describe both the
untwisted and the twisted sectors of the closed string.Comment: 15 pages, LaTeX; v2: added more detail to a derivation, and a
preprint number; v3: minor corrections, some remarks and references adde
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