658 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
Form factors of the XXZ model and the affine quantum group symmetry
We present new expressions of form factors of the XXZ model which satisfy
Smirnov's three axioms. These new form factors are obtained by acting the
affine quantum group to the known ones obtained
in our previous works. We also find the relations among all the new and known
form factors, i.e., all other form factors can be expressed as kind of
descendents of a special one.Comment: 11 pages, latex; Some explanation is adde
Impurity Operators in RSOS Models
We give a construction of impurity operators in the `algebraic analysis'
picture of RSOS models. Physically, these operators are half-infinite
insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue
of insertions of higher spin lines in vertex models. Mathematically, they are
given in terms of intertwiners of modules. We present a
detailed perturbation theory check of the conjectural correspondence between
the physical and mathematical constructions in a particular simple example.Comment: Latex, 24 pages, uses amsmath, amsthm, amssymb, epic, eepic and
texdraw style files (Minor typos corrected) (minor changes
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
Form factor expansion of the row and diagonal correlation functions of the two dimensional Ising model
We derive and prove exponential and form factor expansions of the row
correlation function and the diagonal correlation function of the two
dimensional Ising model
Analytical Bethe Ansatz for quantum-algebra-invariant open spin chains
We determine the eigenvalues of the transfer matrices for integrable open
quantum spin chains which are associated with the affine Lie algebras
, and which have the
quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$,
respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is
removed
The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group
In this paper, we give the general forms of the minimal matrix (the
elements of the -matrix are numbers) associated with the Boltzmann
weights of the interaction-round-a-face (IRF) model and the minimal
representation of the series elliptic quantum group given by Felder
and Varchenko. The explicit dependence of elements of -matrices on spectral
parameter are given. They are of five different forms (A(1-4) and B). The
algebra for the coefficients (which do not depend on ) are given. The
algebra of form A is proved to be trivial, while that of form B obey
Yang-Baxter equation (YBE). We also give the PBW base and the centers for the
algebra of form B.Comment: 23 page
Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields
We show that the transfer matrix of the A_{N-1}^(1) open spin chain with
diagonal boundary fields has the symmetry U_q (SU(L)) x U_q (SU(N-L)) x U(1),
as well as a ``duality'' symmetry which interchanges L and N - L. We exploit
these symmetries to compute exact boundary S matrices in the regime with q
real.Comment: 27 pages, LaTeX, 1 LaTeX figur
A New Solution of the Yang-Baxter Equation Related to the Adjoint Representation of
A new solution of the Yang-Baxter equation, that is related to the adjoint
representation of the quantum enveloping algebra , is obtained by
fusion formulas from a non-standard solution.Comment: 16 pages (Latex), Preprint BIHEP-TH-93-3
Graded q-pseudo-differential Operators and Supersymmetric Algebras
We give a supersymmetric generalization of the sine algebra and the quantum
algebra . Making use of the -pseudo-differential operators
graded with a fermionic algebra, we obtain a supersymmetric extension of sine
algebra. With this scheme we also get a quantum superalgebra .Comment: 10 pages, Late
- …