1,831 research outputs found
Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras
We introduce a functional realization of the Hamiltonian structure on the
moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup
in SL_n. We also introduce a construction of the corresponding quantum
algebras.Comment: 20 pages, Amstex, minor change
Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation
We represent a classical Maxwell-Bloch equation and related to it positive
part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is
given by an infinitesimal action of a nilpotent subalgebra of affine Lie
algebra on a Maxwell-Bloch phase space treated as a homogeneous
space of . A space of local integrals of motion is described using
cohomology methods. We show that hamiltonian flows associated to the
Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are
identified with an infinitesimal action of an abelian subalgebra of the
nilpotent subalgebra on a Maxwell- Bloch phase space. Possibilities of
quantization and latticization of Maxwell-Bloch equation are discussed.Comment: 16 pages, no figures, plain TeX, no macro
Quantum Algebraic Approach to Refined Topological Vertex
We establish the equivalence between the refined topological vertex of
Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of
type W_{1+infty} introduced by Miki. Our construction involves trivalent
intertwining operators Phi and Phi^* associated with triples of the bosonic
Fock modules. Resembling the topological vertex, a triple of vectors in Z^2 is
attached to each intertwining operator, which satisfy the Calabi-Yau and
smoothness conditions. It is shown that certain matrix elements of Phi and
Phi^* give the refined topological vertex C_{lambda mu nu}(t,q) of
Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined
topological vertex C_{lambda mu}^nu(q,t) of Awata-Kanno. The gluing factors
appears correctly when we consider any compositions of Phi and Phi^*. The
spectral parameters attached to Fock spaces play the role of the K"ahler
parameters.Comment: 27 page
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
On Vertex Operator Construction of Quantum Affine Algebras
We describe the construction of the quantum deformed affine Lie algebras
using the vertex operators in the free field theory. We prove the Serre
relations for the quantum deformed Borel subalgebras of affine algebras, namely
the case of is considered in detail. We provide some
formulas for generators of affine algebra.Comment: LaTeX, 9 pages; typos corrected, references adde
Null vectors, 3-point and 4-point functions in conformal field theory
We consider 3-point and 4-point correlation functions in a conformal field
theory with a W-algebra symmetry. Whereas in a theory with only Virasoro
symmetry the three point functions of descendants fields are uniquely
determined by the three point function of the corresponding primary fields this
is not the case for a theory with algebra symmetry. The generic 3-point
functions of W-descendant fields have a countable degree of arbitrariness. We
find, however, that if one of the fields belongs to a representation with null
states that this has implications for the 3-point functions. In particular if
one of the representations is doubly-degenerate then the 3-point function is
determined up to an overall constant. We extend our analysis to 4-point
functions and find that if two of the W-primary fields are doubly degenerate
then the intermediate channels are limited to a finite set and that the
corresponding chiral blocks are determined up to an overall constant. This
corresponds to the existence of a linear differential equation for the chiral
blocks with two completely degenerate fields as has been found in the work of
Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4
Gaudin Model, Bethe Ansatz and Critical Level
We propose a new method of diagonalization of hamiltonians of the Gaudin
model associated to an arbitrary simple Lie algebra, which is based on Wakimoto
modules over affine algebras at the critical level. We construct eigenvectors
of these hamiltonians by restricting certain invariant functionals on tensor
products of Wakimoto modules. In conformal field theory language, the
eigenvectors are given by certain bosonic correlation functions. Analogues of
Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the
existence of certain singular vectors in Wakimoto modules. We use this
construction to expalain a connection between Gaudin's model and correlation
functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected
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