99 research outputs found
From Virasoro Constraints in Kontsevich's Model to -constraints in 2-matrix Models
The Ward identities in Kontsevich-like 1-matrix models are used to prove at
the level of discrete matrix models the suggestion of Gava and Narain, which
relates the degree of potential in asymmetric 2-matrix model to the form of
-constraints imposed on its partition function.Comment: 13 pages (August 1991
WDVV Equations from Algebra of Forms
A class of solutions to the WDVV equations is provided by period matrices of
hyperelliptic Riemann surfaces, with or without punctures. The equations
themselves reflect associativity of explicitly described multiplicative algebra
of (possibly meromorphic) 1-differentials, which holds at least in the
hyperelliptic case. This construction is direct generalization of the old one,
involving the ring of polynomials factorized over an ideal, and is inspired by
the study of the Seiberg-Witten theory. It has potential to be further extended
to reveal algebraic structures underlying the theory of quantum cohomologies
and the prepotentials in string models with N=2 supersymmetry.Comment: LaTeX, 14 pages, no figure
Seiberg-Witten theory for a non-trivial compactification from five to four dimensions
The prepotential and spectral curve are described for a smooth interpolation
between an enlarged N=4 SUSY and ordinary N=2 SUSY Yang-Mills theory in four
dimensions, obtained by compactification from five dimensions with non-trivial
(periodic and antiperiodic) boundary conditions. This system provides a new
solution to the generalized WDVV equations. We show that this exhausts all
possible solutions of a given functional form.Comment: 10 pages, LaTeX, 2 figures using emlines.st
Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
The Kazakov-Migdal model, if considered as a functional of external fields,
can be always represented as an expansion over characters of group. The
integration over "matter fields" can be interpreted as going over the {\it
model} (the space of all highest weight representations) of . In the case
of compact unitary groups the integrals should be substituted by {\it discrete}
sums over weight lattice. The version of the model is the Generalized
Kontsevich integral, which in the above-mentioned unitary (discrete) situation
coincides with partition function of the Yang-Mills theory with the target
space of genus and holes. This particular quantity is always a
bilinear combination of characters and appears to be a Toda-lattice
-function. (This is generalization of the classical statement that
individual characters are always singular KP -functions.) The
corresponding element of the Universal Grassmannian is very simple and somewhat
similar to the one, arising in investigations of the string models.
However, under certain circumstances the formal sum over representations should
be evaluated by steepest descent method and this procedure leads to some more
complicated elements of Grassmannian. This "Kontsevich phase" as opposed to the
simple "character phase" deserves further investigation.Comment: 29 pages, UUITP-10/93, FIAN/TD-07/93, ITEP-M4/9
WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves
We present a generic derivation of the WDVV equations for 6d Seiberg-Witten
theory, and extend it to the families of bi-elliptic spectral curves. We find
that the elliptization of the naive perturbative and nonperturbative 6d systems
roughly "doubles" the number of moduli describing the system.Comment: 24 page
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