382 research outputs found
M-Theory of Matrix Models
Small M-theories unify various models of a given family in the same way as
the M-theory unifies a variety of superstring models. We consider this idea in
application to the family of eigenvalue matrix models: their M-theory unifies
various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition
functions) with Kontsevich tau-function. Moreover, the corresponding duality
relations look like direct analogues of instanton and meron decompositions,
familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical
and Quantum Integrable Systems", Protvino, Russia, January, 200
Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
Even though matrix model partition functions do not exhaust the entire set of
tau-functions relevant for string theory, they seem to be elementary building
blocks for many others and they seem to properly capture the fundamental
symplicial nature of quantum gravity and string theory. We propose to consider
matrix model partition functions as new special functions. This means they
should be investigated and put into some standard form, with no reference to
particular applications. At the same time, the tables and lists of properties
should be full enough to avoid discoveries of unexpected peculiarities in new
applications. This is a big job, and the present paper is just a step in this
direction. Here we restrict our consideration to the finite-size Hermitean
1-matrix model and concentrate mostly on its phase/branch structure arising
when the partition function is considered as a D-module. We discuss the role of
the CIV-DV prepotential (as generating a possible basis in the linear space of
solutions to the Virasoro constraints, but with a lack of understanding of why
and how this basis is distinguished) and evaluate first few multiloop
correlators, which generalize semicircular distribution to the case of
multitrace and non-planar correlators.Comment: 64 pages, LaTe
Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy
We use -component fermions to present -fold
integrals as a fermionic expectation value. This yields fermionic
representation for various -matrix models. Links with the -component
KP hierarchy and also with the -component TL hierarchy are discussed. We
show that the set of all (but two) flows of -component TL changes standard
matrix models to new ones.Comment: 16 pages, submitted to a special issue of Theoretical and
Mathematical Physic
Fermionic approach to the evaluation of integrals of rational symmetric functions
We use the fermionic construction of two-matrix model partition functions to
evaluate integrals over rational symmetric functions. This approach is
complementary to the one used in the paper ``Integrals of Rational Symmetric
Functions, Two-Matrix Models and Biorthogonal Polynomials'' \cite{paper2},
where these integrals were evaluated by a direct method.Comment: 34 page
Challenges of Matrix Models
Brief review of concepts and unsolved problems in the theory of matrix
models.Comment: Contribution to Proceedings of Cargese 200
Non-Linear Algebra and Bogolubov's Recursion
Numerous examples are given of application of Bogolubov's forest formula to
iterative solutions of various non-linear equations: one and the same formula
describes everything, from ordinary quadratic equation to renormalization in
quantum field theory.Comment: LaTex, 21 page
Electroproduction, photoproduction, and inverse electroproduction of pions in the first resonance region
Methods are set forth for determining the hadron electromagnetic structure in
the sub--threshold timelike region of the virtual-photon ``mass'' and
for investigating the nucleon weak structure in the spacelike region from
experimental data on the process at low energies. These
methods are formulated using the unified description of photoproduction,
electroproduction, and inverse electroproduction of pions in the first
resonance region in the framework of the dispersion-relation model and on the
basis of the model-independent properties of inverse electroproduction.
Applications of these methods are also shown.Comment: The revised published version; Revtex4, 18 pages, 6 figure
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