349 research outputs found
QCD, Wick's Theorem for KdV -functions and the String Equation
Two consistency conditions for partition functions established by Akemann and
Dam-gaard in their studies of the fermionic mass dependence of the QCD
partition function at low energy ({\it a la} Leutwiller-Smilga-Verbaarschot)
are interpreted in terms of integrable hierarchies. Their algebraic relation is
shown to be a consequence of Wick's theorem for 2d fermionic correlators
(Hirota identities) in the special case of the 2-reductions of the KP hierarchy
(that is KdV/mKdV). The consistency condition involving derivatives is an
incarnation of the string equation associated with the particular matrix model
(the particular kind of the Kac-Schwarz operator).Comment: 7 pages LaTex. Corrections to grant numbers only for administering
bureaucrat
Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
We introduce {\it conformal multi-matrix models} (CMM) as an alternative to
conventional multi-matrix model description of two-dimensional gravity
interacting with matter. We define CMM as solutions to (discrete)
extended Virasoro constraints. We argue that the so defined alternatives of
multi-matrix models represent the same universality classes in continuum limit,
while at the discrete level they provide explicit solutions to the
multi-component KP hierarchy and by definition satisfy the discrete
-constraints. We prove that discrete CMM coincide with the -series of
2d gravity models in a {\it well}-{\it defined} continuum limit, thus
demonstrating that they provide a proper generalization of Hermitian one-matrix
model.Comment: 35 pages, preprint FIAN/TD-9/92 & ITEP-M-4/9
New matrix model solutions to the Kac-Schwarz problem
We examine the Kac-Schwarz problem of specification of point in Grassmannian
in the restricted case of gap-one first-order differential Kac-Schwarz
operators. While the pair of constraints satisfying always
leads to Kontsevich type models, in the case of the
corresponding KP -functions are represented as more sophisticated matrix
integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the
29th International Symposium Ahrenshoop on the Theory of Elementary
Particles, Buckow, German
On pq-duality and explicit solutions in gravity models
We study the integral representation for the exact solution to
nonperturbative string theory. A generic solution is determined by two
functions and which behaive at infinity like and
respectively. The integral model for arbitrary models is derived which
explicitely demonstrates duality of minimal models coupled to gravity. We
discuss also the exact solutions to string equation and reduction condition and
present several explicit examples.Comment: NORDITA 93/20, FIAN-TD-04/93, latex, 20 p
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