964 research outputs found
Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
The -plane integrals of topologically twisted supersymmetric gauge
theories generally contain contact terms of nonlocal topological observables.
This paper proposes an interpretation of these contact terms from the point of
view of integrable hierarchies and their Whitham deformations. This is inspired
by Mari\~no and Moore's remark that the blowup formula of the -plane
integral contains a piece that can be interpreted as a single-time tau function
of an integrable hierarchy. This single-time tau function can be extended to a
multi-time version without spoiling the modular invariance of the blowup
formula. The multi-time tau function is comprised of a Gaussian factor
and a theta function. The time variables play the
role of physical coupling constants of 2-observables carried by the
exceptional divisor . The coefficients of the Gaussian part are
identified to be the contact terms of these 2-observables. This identification
is further examined in the language of Whitham equations. All relevant
quantities are written in the form of derivatives of the prepotential.Comment: latex, 17 pages, no figures; final version for publicatio
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
Toda Lattice Hierarchy and Zamolodchikov's Conjecture
In this letter, we show that certain Fredholm determinant ,
introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit
of soliton solution for the Toda lattice hierarchy with 2-periodic reduction
condition.Comment: 6 pages, LaTeX file, no figure
Fusion of the -Vertex Operators and its Application to Solvable Vertex Models
We diagonalize the transfer matrix of the inhomogeneous vertex models of the
6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex
operators. The special cases of those models were used to diagonalize the s-d
exchange model\cite{W,A,FW1}. New vertex operators are constructed from the
level one vertex operators by the fusion procedure and have the description by
bosons. In order to clarify the particle structure we estabish new isomorphisms
of crystals. The results are very simple and figure out representation
theoretically the ground state degenerations.Comment: 35 page
Annihilation poles of a Smirnov-type integral formula for solutions to quantum Knizhnik--Zamolodchikov equation
We consider the recently obtained integral representation of quantum
Knizhnik-Zamolodchikov equation of level 0. We obtain the condition for the
integral kernel such that these solutions satisfy three axioms for form factor
\'{a} la Smirnov. We discuss the relation between this integral representation
and the form factor of XXZ spin chain.Comment: 14 pages, latex, no figures
Difference equations for the higher rank XXZ model with a boundary
The higher rank analogue of the XXZ model with a boundary is considered on
the basis of the vertex operator approach. We derive difference equations of
the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model.
We present infinite product formulae of two point functions with free boundary
condition by solving those difference equations with N=1.Comment: LaTEX 16 page
Notes on highest weight modules of the elliptic algebra
We discuss a construction of highest weight modules for the recently defined
elliptic algebra , and make several conjectures
concerning them. The modules are generated by the action of the components of
the operator on the highest weight vectors. We introduce the vertex
operators and through their commutation relations with the
-operator. We present ordering rules for the - and -operators and
find an upper bound for the number of linearly independent vectors generated by
them, which agrees with the known characters of -modules.Comment: Nonstandard macro package eliminate
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