157 research outputs found
Planar Gravitational Corrections For Supersymmetric Gauge Theories
In this paper we discuss the contribution of planar diagrams to gravitational
F-terms for N=1 supersymmetric gauge theories admitting a large N description.
We show how the planar diagrams lead to a universal contribution at the
extremum of the glueball superpotential, leaving only the genus one
contributions, as was previously conjectured. We also discuss the physical
meaning of gravitational F-terms.Comment: 20 pages, 4 figure
Perturbative Computation of Glueball Superpotentials
Using N=1 superspace techniques in four dimensions we show how to
perturbatively compute the superpotential generated for the glueball superfield
upon integrating out massive charged fields. The technique applies to arbitrary
gauge groups and representations. Moreover we show that for U(N) gauge theories
admitting a large N expansion the computation dramatically simplifies and we
prove the validity of the recently proposed recipe for computation of this
quantity in terms of planar diagrams of matrix integrals.Comment: 15 Pages, 2 Figure
Topological Phase Transitions and Holonomies in the Dimer Model
We demonstrate that the classical dimer model defined on a toroidal hexagonal
lattice acquires holonomy phases in the thermodynamic limit. When all
activities are equal the lattice sizes must be considered mod 6 in which case
the finite size corrections to the bulk partition function correspond to a
massless Dirac Fermion in the presence of a flat connection with nontrivial
holonomy. For general bond activities we find that the phase transition in this
model is a topological one, where the torus degenerates and its modular
parameter becomes real at the critical temperature. We argue that these
features are generic to bipartite dimer models and we present a more general
lattice whose continuum partition function is that of a massive Dirac Fermion.Comment: 7 pages, 4 figures. Minor corrections with additional figure
Black Holes and Large Order Quantum Geometry
We study five-dimensional black holes obtained by compactifying M theory on
Calabi-Yau threefolds. Recent progress in solving topological string theory on
compact, one-parameter models allows us to test numerically various conjectures
about these black holes. We give convincing evidence that a microscopic
description based on Gopakumar-Vafa invariants accounts correctly for their
macroscopic entropy, and we check that highly nontrivial cancellations -which
seem necessary to resolve the so-called entropy enigma in the OSV conjecture-
do in fact occur. We also study analytically small 5d black holes obtained by
wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II
duality we obtain exact formulae for the microscopic degeneracies in various
geometries, and we compute their asymptotic expansion for large charges.Comment: 42 pages, 20 eps figures, small correction
Gravitational corrections in supersymmetric gauge theory and matrix models
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur
Superpotentials from flux compactifications of M-theory
In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page
The M5-Brane Elliptic Genus: Modularity and BPS States
The modified elliptic genus for an M5-brane wrapped on a four-cycle of a
Calabi-Yau threefold encodes the degeneracies of an infinite set of BPS states
in four dimensions. By holomorphy and modular invariance, it can be determined
completely from the knowledge of a finite set of such BPS states. We show the
feasibility of such a computation and determine the exact modified elliptic
genus for an M5-brane wrapping a hyperplane section of the quintic threefold.Comment: 21 page
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
We show that various holomorphic quantities in supersymmetric gauge theories
can be conveniently computed by configurations of D4-branes and D6-branes.
These D-branes intersect along a Riemann surface that is described by a
holomorphic curve in a complex surface. The resulting I-brane carries
two-dimensional chiral fermions on its world-volume. This system can be mapped
directly to the topological string on a large class of non-compact Calabi-Yau
manifolds. Inclusion of the string coupling constant corresponds to turning on
a constant B-field on the complex surface, which makes this space
non-commutative. Including all string loop corrections the free fermion theory
is elegantly formulated in terms of holonomic D-modules that replace the
classical holomorphic curve in the quantum case.Comment: 67 pages, 6 figure
Polynomial rings of the chiral models
Via explicit diagonalization of the chiral fusion matrices, we
discuss the possibility of representing the fusion ring of the chiral SU(N)
models, at level K=2, by a polynomial ring in a single variable when is odd
and by a polynomial ring in two variables when is even.Comment: 10 pages, LaTex (ioplppt.sty
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