2,000 research outputs found
The Mathematics of Fivebranes
Fivebranes are non-perturbative objects in string theory that generalize
two-dimensional conformal field theory and relate such diverse subjects as
moduli spaces of vector bundles on surfaces, automorphic forms, elliptic
genera, the geometry of Calabi-Yau threefolds, and generalized Kac-Moody
algebras.Comment: 10 pages, 2 figures, Lecture at ICM'9
Determinant Formulas for Matrix Model Free Energy
The paper contains a new non-perturbative representation for subleading
contribution to the free energy of multicut solution for hermitian matrix
model. This representation is a generalisation of the formula, proposed by
Klemm, Marino and Theisen for two cut solution, which was obtained by comparing
the cubic matrix model with the topological B-model on the local Calabi-Yau
geometry and was checked perturbatively. In this paper we give a
direct proof of their formula and generalise it to the general multicut
solution.Comment: 5 pages, submitted to JETP Letters, references added, minor
correction
Balanced Topological Field Theories
We describe a class of topological field theories called ``balanced
topological field theories.'' These theories are associated to moduli problems
with vanishing virtual dimension and calculate the Euler character of various
moduli spaces. We show that these theories are closely related to the geometry
and equivariant cohomology of ``iterated superspaces'' that carry two
differentials. We find the most general action for these theories, which turns
out to define Morse theory on field space. We illustrate the constructions with
numerous examples. Finally, we relate these theories to topological
sigma-models twisted using an isometry of the target space.Comment: 40 pages, harvmac, references added, to appear in Commun. Math. Phy
Holomorphic matrix models
This is a study of holomorphic matrix models, the matrix models which
underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic
description of the holomorphic one-matrix model. After discussing its
convergence sectors, I show that certain puzzles related to its perturbative
expansion admit a simple resolution in the holomorphic set-up. Constructing a
`complex' microcanonical ensemble, I check that the basic requirements of the
conjecture (in particular, the special geometry relations involving chemical
potentials) hold in the absence of the hermicity constraint. I also show that
planar solutions of the holomorphic model probe the entire moduli space of the
associated algebraic curve. Finally, I give a brief discussion of holomorphic
models, focusing on the example of the quiver, for which I extract
explicitly the relevant Riemann surface. In this case, use of the holomorphic
model is crucial, since the Hermitian approach and its attending regularization
would lead to a singular algebraic curve, thus contradicting the requirements
of the conjecture. In particular, I show how an appropriate regularization of
the holomorphic model produces the desired smooth Riemann surface in the
limit when the regulator is removed, and that this limit can be described as a
statistical ensemble of `reduced' holomorphic models.Comment: 45 pages, reference adde
The partition function of 2d string theory
We derive a compact and explicit expression for the generating functional of
all correlation functions of tachyon operators in 2D string theory. This
expression makes manifest relations of the system to KP flow and
constraints. Moreover we derive a Kontsevich-Penner integral
representation of this generating functional.Comment: 28 pages, 3 figures not included, harvmac. Preprint IASSNS-HEP-92/48,
YCTP-P22-9
Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
We show how the Dijkgraaf-Vafa matrix model proposal can be extended to
describe five-dimensional gauge theories compactified on a circle to four
dimensions. This involves solving a certain quantum mechanical matrix model. We
do this for the lift of the N=1* theory to five dimensions. We show that the
resulting expression for the superpotential in the confining vacuum is
identical with the elliptic superpotential approach based on Nekrasov's
five-dimensional generalization of Seiberg-Witten theory involving the
relativistic elliptic Calogero-Moser, or Ruijsenaars-Schneider, integrable
system.Comment: 11 pages, 2 figures, JHEP3.cls, important references adde
Another Leigh-Strassler deformation through the Matrix model
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to
obtain the effective superpotential for a certain deformation of N=4 SYM
discovered by Leigh and Strassler. An exact solution to the matrix model
Lagrangian is found and is expressed in terms of elliptic functions.Comment: 15 pages,2 figure
On the partition sum of the NS five-brane
We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a
double-scaled decoupling limit. We calculate the euclidean partition function
in the presence of a flat RR 3-form field. The classical contribution is given
by a sum over fluxes of the self-dual tensor field which reduces to a
theta-function. The quantum contributions are computed using a T-dual IIB
background where the five-branes are replaced by an ALE singularity. Using the
supergravity effective action we find that the loop corrections to the free
energy are given by B-model topological string amplitudes. This seems to
provide a direct link between the double-scaled little strings on the
five-brane worldvolume and topological strings. Both the classical and quantum
contributions to the partition function satisfy (conjugate) holomorphic anomaly
equations, which explains an observation of Witten relating topological string
theory to the quantization of three-form fields.Comment: 35 page
On the Matter of the Dijkgraaf--Vafa Conjecture
With the aim of extending the gauge theory -- matrix model connection to more
general matter representations, we prove that for various two-index tensors of
the classical gauge groups, the perturbative contributions to the glueball
superpotential reduce to matrix integrals. Contributing diagrams consist of
certain combinations of spheres, disks, and projective planes, which we
evaluate to four and five loop order. In the case of with antisymmetric
matter, independent results are obtained by computing the nonperturbative
superpotential for and 8. Comparison with the Dijkgraaf-Vafa approach
reveals agreement up to loops in matrix model perturbation theory, with
disagreement setting in at loops, being the dual Coxeter number.
At this order, the glueball superfield begins to obey nontrivial relations
due to its underlying structure as a product of fermionic superfields. We
therefore find a relatively simple example of an gauge theory
admitting a large expansion, whose dynamically generated superpotential
differs from the one obtained in the matrix model approach.Comment: 20 pages, harvmac. v2: added comments and reference
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