1,959 research outputs found
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
Konishi anomaly and N=1 effective superpotentials from matrix models
We discuss the restrictions imposed by the Konishi anomaly on the matrix
model approach to the calculation of the effective superpotentials in N=1 SUSY
gauge theories with different matter content. It is shown that they correspond
to the anomaly deformed Virasoro constraints .Comment: Latex, 8 pages, misprint and the normalization of the condensate in
the elliptic model are correcte
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
Effective matter superpotentials from Wishart random matrices
We show how within the Dijkgraaf-Vafa prescription one can derive
superpotentials for matter fields. The ingredients forming the non-perturbative
Affleck-Dine-Seiberg superpotentials arise from constrained matrix integrals,
which are equivalent to classical complex Wishart random matrices. The
mechanism is similar to the way the Veneziano-Yankielowicz superpotential
arises from the matrix model measure.Comment: 9 pages; v2: published versio
2D String Theory as Normal Matrix Model
We show that the bosonic string theory at finite temperature has two
matrix-model realizations related by a kind of duality transformation. The
first realization is the standard one given by the compactified matrix quantum
mechanics in the inverted oscillator potential. The second realization, which
we derive here, is given by the normal matrix model. Both matrix models exhibit
the Toda integrable structure and are associated with two dual cycles (a
compact and a non-compact one) of a complex curve with the topology of a sphere
with two punctures. The equivalence of the two matrix models holds for an
arbitrary tachyon perturbation and in all orders in the string coupling
constant.Comment: lanlmac, 21 page
On Equivalence of Topological and Quantum 2d Gravity
We demonstrate the equivalence of Virasoro constraints imposed on continuum
limit of partition function of Hermitean 1-matrix model and the Ward identities
of Kontsevich's model. Since the first model describes ordinary quantum
gravity, while the second one is supposed to coincide with Witten's topological
gravity, the result provides a strong implication that the two models are
indeed the same.Comment: 14 pages (August 1991
Baby Universes in String Theory
We argue that the holographic description of four-dimensional BPS black holes
naturally includes multi-center solutions. This suggests that the holographic
dual to the gauge theory is not a single AdS_2 times S^2 but a coherent
ensemble of them. We verify this in a particular class of examples, where the
two-dimensional Yang-Mills theory gives a holographic description of the black
holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic
formulation, we show that O(e^{-N}) non-perturbative effects entangle the two
Fermi surfaces. In an Euclidean description, the wave-function of the
multi-center black holes gets mapped to the Hartle-Hawking wave-function of
baby universes. This provides a concrete realization, within string theory, of
effects that can be interpreted as the creation of baby universes. We find
that, at least in the case we study, the baby universes do not lead to a loss
of quantum coherence, in accord with general arguments.Comment: 39 pages, 7 figure
Perturbative analysis of gauged matrix models
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that nonperturbative aspects of [script N] = 1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for [script N] = 2 gauge theory, the Montonen-Olive modular invariance for [script N] = 1*, and the superpotential for the Leigh-Strassler deformation of [script N] = 4 can be systematically computed in perturbation theory of the matrix model or gauge theory (even though in some of these cases an exact answer can also be obtained by summing up planar diagrams of matrix models)
Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
In the framework of the matrix model/gauge theory correspondence, we consider
supersymmetric U(N) gauge theory with symmetry breaking pattern. Due
to the presence of the Veneziano--Yankielowicz effective superpotential, in
order to satisfy the --term condition , we are forced to
introduce additional terms in the free energy of the corresponding matrix model
with respect to the usual formulation. This leads to a matrix model formulation
with a cubic potential which is free of parameters and displays a branched
structure. In this way we naturally solve the usual problem of the
identification between dimensionful and dimensionless quantities. Furthermore,
we need not introduce the scale by hand in the matrix model. These facts
are related to remarkable coincidences which arise at the critical point and
lead to a branched bare coupling constant. The latter plays the role of the
and scale tuning parameter. We then show that a suitable
rescaling leads to the correct identification of the variables. Finally,
by means of the the mentioned coincidences, we provide a direct expression for
the prepotential, including the gravitational corrections, in terms of
the free energy. This suggests that the matrix model provides a triangulation
of the istanton moduli space.Comment: 1+18 pages, harvmac. Added discussion on the CSW relative shifts of
theta vacua and the odd phases at the critical point. References added and
typos correcte
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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