1,091 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
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
Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity
In a previous work, it was shown that the 8-dimensional topological quantum
field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1
D = 8 supergravity. It is shown here that, the combination of this TQFT with
that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated
dimensional reduction of N = 1 D = 11 supergravity. Our construction holds for
8-dimensional manifolds with Spin(7) \subset SO(8) holonomy. We suggest that
the origin of local Poincare supersymmetry is the gravitational topological
symmetry. We indicate a mechanism for the lift of the TQFT in higher
dimensions, which generates Chern-Simons couplings.Comment: one section has been adde
String Interactions from Matrix String Theory
The Matrix String Theory, i.e. the two dimensional U(N) SYM with N=(8,8)
supersymmetry, has classical BPS solutions that interpolate between an initial
and a final string configuration via a bordered Riemann surface. The Matrix
String Theory amplitudes around such a classical BPS background, in the strong
Yang--Mills coupling, are therefore candidates to be interpreted in a stringy
way as the transition amplitude between given initial and final string
configurations. In this paper we calculate these amplitudes and show that the
leading contribution is proportional to the factor g_s^{-\chi}, where \chi is
the Euler characteristic of the interpolating Riemann surface and g_s is the
string coupling. This is the factor one expects from perturbative string
interaction theory.Comment: 15 pages, 2 eps figures, JHEP Latex class, misprints correcte
Matrix Model for Discretized Moduli Space
We study the algebraic geometrical background of the Penner--Kontsevich
matrix model with the potential N\alpha \tr {\bigl(- \fr 12 \L X\L X +\log
(1-X)+X\bigr)}. We show that this model describes intersection indices of
linear bundles on the discretized moduli space right in the same fashion as the
Kontsevich model is related to intersection indices (cohomological classes) on
the Riemann surfaces of arbitrary genera. The special role of the logarithmic
potential originated from the Penner matrix model is demonstrated. The boundary
effects which was unessential in the case of the Kontsevich model are now
relevant, and intersection indices on the discretized moduli space of genus
are expressed through Kontsevich's indices of the genus and of the lower
genera
Flavour from partially resolved singularities
In this letter we study topological open string field theory on D--branes in
a IIB background given by non compact CY geometries on with a singular point at which an extra fiber sits. We wrap
D5-branes on and effective D3-branes at singular points, which
are actually D5--branes wrapped on a shrinking cycle. We calculate the
holomorphic Chern-Simons partition function for the above models in a deformed
complex structure and find that it reduces to multi--matrix models with
flavour. These are the matrix models whose resolvents have been shown to
satisfy the generalized Konishi anomaly equations with flavour. In the
case, corresponding to a partial resolution of the singularity, the
quantum superpotential in the unitary SYM with one adjoint and
fundamentals is obtained. The case is also studied and shown to give rise
to two--matrix models which for a particular set of couplings can be exactly
solved. We explicitly show how to solve such a class of models by a quantum
equation of motion technique
Reconstruction of N=1 supersymmetry from topological symmetry
The scalar and vector topological Yang-Mills symmetries on Calabi-Yau
manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1
supersymmetry, which fully determine the supersymmetric actions up to twist.
For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory
can be reconstructed in this way. A superpotential can be introduced for the
matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold,
the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting
these results together with those already known for the D=4,8 N=2 cases, we
conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are
determined from topological symmetry on special manifolds.Comment: 13 page
Baryonic Corrections to Superpotentials from Perturbation Theory
We study the corrections induced by a baryon vertex to the superpotential of
SQCD with gauge group SU(N) and N quark flavors. We first compute the
corrections order by order using a standard field theory technique and derive
the corresponding glueball superpotential by "integrating in" the glueball
field. The structure of the corrections matches with the expectations from the
recently introduced perturbative techniques. We then compute the first
non-trivial contribution using this new technique and find exact quantitative
agreement. This involves cancellations between diagrams that go beyond the
planar approximation.Comment: 8 page
Crossings, Motzkin paths and Moments
Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain
-analogues of Laguerre and Charlier polynomials. The moments of these
orthogonal polynomials have combinatorial models in terms of crossings in
permutations and set partitions. The aim of this article is to prove simple
formulas for the moments of the -Laguerre and the -Charlier polynomials,
in the style of the Touchard-Riordan formula (which gives the moments of some
-Hermite polynomials, and also the distribution of crossings in matchings).
Our method mainly consists in the enumeration of weighted Motzkin paths, which
are naturally associated with the moments. Some steps are bijective, in
particular we describe a decomposition of paths which generalises a previous
construction of Penaud for the case of the Touchard-Riordan formula. There are
also some non-bijective steps using basic hypergeometric series, and continued
fractions or, alternatively, functional equations.Comment: 21 page
Topological Field Theory Interpretations and LG Representation of c=1 String Theory
We analyze the topological nature of string theory at the self--dual
radius. We find that it admits two distinct topological field theory structures
characterized by two different puncture operators. We show it first in the
unperturbed theory in which the only parameter is the cosmological constant,
then in the presence of any infinitesimal tachyonic perturbation. We also
discuss in detail a Landau--Ginzburg representation of one of the two
topological field theory structures.Comment: 25 pages, LaTeX, report number adde
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