3,400 research outputs found
Restricted Quantum Affine Symmetry of Perturbed Minimal Models
We study the structure of superselection sectors of an arbitrary perturbation
of a conformal field theory. We describe how a restriction of the q-deformed
affine Lie algebra symmetry of the sine-Gordon theory can be used
to derive the S-matrices of the perturbations of the minimal
unitary series. This analysis provides an identification of fields which create
the massive kink spectrum. We investigate the ultraviolet limit of the
restricted sine-Gordon model, and explain the relation between the restriction
and the Fock space cohomology of minimal models. We also comment on the
structure of degenerate vacuum states. Deformed Serre relations are proven for
arbitrary affine Toda theories, and it is shown in certain cases how relations
of the Serre type become fractional spin supersymmetry relations upon
restriction.Comment: 40 page
Special functions, conformal blocks, Bethe ansatz, and SL(3,Z)
This is the talk of the second author at the meeting "Topological Methods in
Physical Sciences", London, November 2000. We review our work on KZB equations.Comment: 10 pages, AMSLaTe
Deformation quantization with generators and relations
In this paper we prove a conjecture of B. Shoikhet which claims that two
quantization procedures arising from Fourier dual constructions actually
coincide.Comment: 9 pages; 4 figures; many typos have been corrected; the introduction
has been considerably extended and a more detailed exposition of the Koszul
theory behind the main idea has been added; the proof of Proposition 2.4
(iii) has been also extended; Subsection 3.2 has been enlarged, and a more
detailed exposition of how the Duflo element arises has been adde
Vertex Operators for Deformed Virasoro Algebra
Vertex operators for the deformed Virasoro algebra are defined, their bosonic
representation is constructed and difference equation for the simplest vertex
operators is described.Comment: stylistic errors correcte
Elliptic Dunkl operators, root systems, and functional equations
We consider generalizations of Dunkl's differential-difference operators
associated with groups generated by reflections. The commutativity condition is
equivalent to certain functional equations. These equations are solved in many
cases. In particular, solutions associated with elliptic curves are
constructed. In the case, we discuss the relation with elliptic
Calogero-Moser integrable -body problems, and discuss the quantization
(-analogue) of our construction.Comment: 30 page
Inhomogeneous Fragmentation of the Rolling Tachyon
Dirac-Born-Infeld type effective actions reproduce many aspects of string
theory classical tachyon dynamics of unstable Dp-branes. The inhomogeneous
tachyon field rolling from the top of its potential forms topological defects
of lower codimensions. In between them, as we show, the tachyon energy density
fragments into a p-dimensional web-like high density network evolving with
time. We present an analytic asymptotic series solution of the non-linear
equations for the inhomogeneous tachyon and its stress energy. The generic
solution for a tachyon field with a runaway potential in arbitrary dimensions
is described by the free streaming of noninteracting massive particles whose
initial velocities are defined by the gradients of the initial tachyon profile.
Thus, relativistic particle mechanics is a dual picture of the tachyon field
effective action. Implications of this picture for inflationary models with a
decaying tachyon field are discussed.Comment: 10 pages, 1 figur
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