Related papers: Form factors, correlation functions and vertex ope…
A model with a scalar type eight-fermion interaction is investigated in curved spacetime. The ground state of the model can be obtained by observing the effective potential. Applying the Riemann normal coordinate expansion, we calculate an…
Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula.…
We study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let $B$…
We conjecture the inversion relations for thermalized solvable interaction round the face (IRF) two dimensional lattice models. We base ourselves on an ansatz for the Baxterization described by the author in the 90's. We solve these…
A class theorem is presented and proved: the complex Fourier transforms of a certain class of exponential functions have all their zeros on the real line. A class of basis functions is first considered, and the class is then extended via…
It is known from Zhu's results that under modular transformations, correlators of rational $C_2$-cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that…
We extend the concept of conjugate vertex operators, first introduced by Dotsenko in the case of the bosonization of the $su(2)$ conformal field theory, to the bosonization of the dynamical vertex operators (type II in the classification of…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed and difference equation for the simplest vertex operators is described.
We extend the recent approach of M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki to derive an integral formula for the N-point correlation functions of arbitrary local operators of the antiferromagnetic spin-1 XXZ model. For this, we realize…
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…
We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible…
We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
We study the properties of reflectionless measures for an $s$-dimensional Calder\'on-Zygmund operator $T$ acting in $\mathbb{R}^d$, where $s\in (0,d)$. Roughly speaking, these are the measures $\mu$ for which $T(\mu)$ is constant on the…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
A formula is proposed which expresses free fermion fields in 2K dimensions in terms of the Cartan currents of the free fermion current algebra. This leads, in an obvious manner, to a vertex operator construction of nonabelian free fermion…
The nearest neighbor two-point correlation function of the $Z$-invariant inhomogeneous eight-vertex model in the thermodynamic limit is computed using the free field representation.
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to…