A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Elliptic Deformed Superalgebra uq,p(sl^(M∣N))u_{q,p}(\hat{{sl}}(M|N))

We introduce the elliptic superalgebra $U_{q,p}(\hat{sl}(M|N))$ as one parameter deformation of the quantum superalgebra $U_q(\hat{sl}(M|N))$. For an arbitrary level $k \neq 1$ we give the bosonization of the elliptic superalgebra $U_{q,p}(\hat{sl}(1|2))$ and the screening currents that commute with $U_{q,p}(\hat{sl}(1|2))$ modulo total difference.Comment: LaTEX, 25 page

Dual Resonance Model Solves the Yang-Baxter Equation

The duality of dual resonance models is shown to imply that the four point string correlation function solves the Yang-Baxter equation. A reduction of transfer matrices to $A_l$ symmetry is described by a restriction of the KP $\tau$ function to Toda molecules.Comment: 10 pages, LaTe

Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable chiral Potts spin chain for chains of length 3,4,5. From these results we present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update

ESR investigation on the Breather mode and the Spinon-Breather dynamical crossover in Cu Benzoate

A new elementary-excitation, the so called "breather excitation", is observed directly by millimeter-submillimeter wave electron spin resonance (ESR) in the Heisenberg quantum spin-chain Cu benzoate, in which a field-induced gap is found recently by specific heat and neutron scattering measurements. Distinct anomalies were found in line width and in resonance field around the "dynamical crossover" regime between the gap-less spinon-regime and the gapped breather-regime. When the temperature becomes sufficiently lower than the energy gap, a new ESR-line with very narrow line-width is found, which is the manifestation of the breather excitation. The non-linear field dependence of the resonance field agrees well with the theoretical formula of the first breather-excitation proposed by Oshikawa and Affleck. The present work establishes experimentally for the first time that a sine-Gordon model is applicable to explain spin dynamics in a S=1/2 Heisenberg spin chain subjected to staggered field even in high fields.Comment: Revtex, 4 pages, 4 figures, submitted to Phys. Rev. Let

Additional symmetries of constrained CKP and BKP hierarchies

The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly. Furthermore, we show that acting on the space of the wave operator, $\partial_k^*$ forms new centerless $W^{cC}_{1+\infty}$ and $W^{cB}_{1+\infty}$-subalgebra of centerless $W_{1+\infty}$ respectively. In order to define above symmetry flows $\partial_k^*$ of the cCKP and cBKP hierarchies, two vital operators $Y_k$ are introduced to revise the additional symmetry flows of the CKP and BKP hierarchies.Comment: 14 pages, accepted by SCIENCE CHINA Mathematics(2010

Field of a Radiation Distributuion

General relativistic spherically symmetric matter field with a vanishing stress energy scalar is analyzed. Procedure for generating exact solutions of the field equations for such matter distributions is given. It is further pointed out that all such type I spherically symmetric fields with distinct eignvalues in the radial two space can be treated as a mixture of isotropic and directed radiations. Various classes of exact solutions are given. Junction conditions for such a matter field to the possible exterior solutions are also discussed.Comment: Latex file, 13 pages, no figures. Accepted for publication in Phys. Rev.

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Are Bosonic Replicas Faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.Comment: 4.3 pages; final version to appear in PR

The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio