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We obtain a new multiple integral representation for the spin-spin correlation functions of the XXZ spin-1/2 infinite chain. We show that this representation is closely related with the partition function of the six-vertex model with domain…
We give a brief review of our approach to the quantization of superstrings. New is a covariant derivation of the measure at tree level and a path integral formula for this measure.
An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…
In this paper we first establish several integral identities. These integrals are of the form \[\int_0^1 x^{an+b} f(x)\,dx\quad (a\in\{1,2\},\ b\in\{-1,-2\})\] where $f(x)$ is a single-variable multiple polylogarithm function or…
Some new identities for Schur functions are proved. In particular, we settle in the affirmative a recent conjecture of Ishikawa-Wakayama and solve a problem raised by Bressoud.
We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies…
We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given…
In the calculation of hot-plasma atomic structure, the continuum wavefunctions are characterized by phase shifts, which therefore determine the scattering cross-sections. In this short paper, we propose a recurrence relation for the phase…
Recently dilogarithm identities have made their appearance in the physics literature. These identities seem to allow to calculate structure constants like, in particular, the effective central charge of certain conformal field theories from…
First-principles descriptions of correlated quantum materials require a simultaneous treatment of strong local many-body effects and nonlocal dynamical screening. We present an efficient fully self-consistent implementation of $GW$+EDMFT…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum…
In this paper we discuss a universal integrable model, given by a sum of two Wess-Zumino-Witten-Novikov (WZWN) actions, corresponding to two different orbits of the coadjoint action of a loop group on its dual, and the Polyakov-Weigmann…
A generalized Wakimoto realization of $\widehat{\cal G}_K$ can be associated with each parabolic subalgebra ${\cal P}=({\cal G}_0 +{\cal G}_+)$ of a simple Lie algebra ${\cal G}$ according to an earlier proposal by Feigin and Frenkel. In…
In this paper we formulate combinatorial identities that give representation of positive integers as linear combination of even powers of 2 with binomial coefficients. We present side by side combinatorial as well as computer generated…
After defining in detail the Lambert $W$-function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so,…
We show that the WZNW model with arbitrary $\sigma$-model coupling constant may be viewed as a $\sigma$-model perturbation of the WZNW theory around the Witten conformal point. In order for the $\sigma$-model perturbation to be relevant,…
We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories…