68 research outputs found
Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures
In this paper we examine the bi-Hamiltonian structure of the generalized
KdV-hierarchies. We verify that both Hamiltonian structures take the form of
Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated
system. Classical extended conformal algebras are obtained from the second
Poisson bracket. In particular, we construct the algebras, first
discussed for the case and by A. Polyakov and M. Bershadsky.Comment: 41 page
Crystallization of random trigonometric polynomials
We give a precise measure of the rate at which repeated differentiation of a
random trigonometric polynomial causes the roots of the function to approach
equal spacing. This can be viewed as a toy model of crystallization in one
dimension. In particular we determine the asymptotics of the distribution of
the roots around the crystalline configuration and find that the distribution
is not Gaussian.Comment: 10 pages, 3 figure
Covariant Closed String Coherent States
We give the first construction of covariant coherent closed string states,
which may be identified with fundamental cosmic strings. We outline the
requirements for a string state to describe a cosmic string, and using DDF
operators provide an explicit and simple map that relates three different
descriptions: classical strings, lightcone gauge quantum states and covariant
vertex operators. The naive construction leads to covariant vertex operators
whose existence requires a lightlike compactification of spacetime. When the
lightlike compactified states in the underlying Hilbert space are projected out
the resulting coherent states have a classical interpretation and are in
one-to-one correspondence with arbitrary classical closed string loops.Comment: 4 page
Type-I Quantum Superalgebras, -Supertrace and Two-variable Link Polynomials
A new general eigenvalue formula for the eigenvalues of Casimir invariants,
for the type-I quantum superalgebras, is applied to the construction of link
polynomials associated with {\em any} finite dimensional unitary irrep for
these algebras. This affords a systematic construction of new two-variable link
polynomials asociated with any finite dimensional irrep (with a real highest
weight) for the type-I quantum superalgebras. In particular infinite families
of non-equivalent two-variable link polynomials are determined in fully
explicit form.Comment: the version to be published in J. Math. Phy
On the Classification of Diagonal Coset Modular Invariants
We relate in a novel way the modular matrices of GKO diagonal cosets without
fixed points to those of WZNW tensor products. Using this we classify all
modular invariant partition functions of
for all positive integer level , and for all and infinitely many (in fact, for
each a positive density of ). Of all these classifications, only that
for had been known. Our lists include many
new invariants.Comment: 24 pp (plain tex
Twisted Current Algebra: Free Field Representation and Screening Currents
Motivated by applications of twisted current algebras in description of the
entropy of black hole, we investigate the simplest twisted current
algebra . Free field representation of the twisted
algebra and the corresponding twisted Sugawara energy-momentum tensor are
obtained by using three pairs and two scalar fields. Primary
fields and two screening currents of the first kind are presented.Comment: LaTex file 12 pages; Final version for publication in Phys. Letts. B
(a couple of typos on page 7 have been corrected in this version
X=M for symmetric powers
The X=M conjecture of Hatayama et al. asserts the equality between the
one-dimensional configuration sum X expressed as the generating function of
crystal paths with energy statistics and the fermionic formula M for all affine
Kac--Moody algebra. In this paper we prove the X=M conjecture for tensor
products of Kirillov--Reshetikhin crystals B^{1,s} associated to symmetric
powers for all nonexceptional affine algebras.Comment: 40 pages; to appear in J. Algebr
Demazure structure inside Kirillov-Reshetikhin crystals
The conjecturally perfect Kirillov-Reshetikhin (KR) crystals are known to be
isomorphic as classical crystals to certain Demazure subcrystals of crystal
graphs of irreducible highest weight modules over affine algebras. Under some
assumptions we show that the classical isomorphism from the Demazure crystal to
the KR crystal, sends zero arrows to zero arrows. This implies that the affine
crystal structure on these KR crystals is unique.Comment: 17 page
The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian
The space of all solutions to the string equation of the symmetric unitary
one-matrix model is determined. It is shown that the string equation is
equivalent to simple conditions on points and in the big cell \Gr
of the Sato Grassmannian . This is a consequence of a well-defined
continuum limit in which the string equation has the simple form \lb \cp
,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- matrices of
differential operators. These conditions on and yield a simple
system of first order differential equations whose analysis determines the
space of all solutions to the string equation. This geometric formulation leads
directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate
the two modified-KdV \t-functions whose product gives the partition function
of the Unitary Matrix Model.Comment: 21 page
Current Superalgebra and Non-unitary Conformal Field Theory
Motivated by application of current superalgebras in the study of disordered
systems such as the random XY and Dirac models, we investigate
current superalgebra at general level . We construct its free field
representation and corresponding Sugawara energy-momentum tensor in the
non-standard basis. Three screen currents of the first kind are also presented.Comment: LaTex file 11 page
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