Related papers: Modular differential equations for torus one-point…
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
A simple realization of the conformal higher spin symmetry on the free $3d$ massless matter fields is given in terms of an auxiliary Fock module both in the flat and $AdS_3$ case. The duality between non-unitary field-theoretical…
Topological 1-soliton solutions to various conformable fractional PDEs in both one and more dimensions are constructed by using simple hyperbolic function ansatz. Suitable traveling wave transformation reduces the fractional partial…
We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.
In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
We provide explicit partial differential equations - in finite cases - and functional differential equations - in field-theoretic cases - which determine observables or beables in the senses of Kucha\v{r} and of Dirac. These cover a wide…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…
We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
We give an implicit equation for the accessory parameter on the torus which is the necessary and sufficient condition to obtain the monodromy of the conformal factor. It is shown that the perturbative series for the accessory parameter in…
Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category $\mathcal{C}$ and a central charge $c$. A long-term goal is to classify unitary rational conformal field theories…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…