Related papers: Crossing invariant correlation functions at $c=1$ …

We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent…

A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent…

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational,…

Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…

We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a…

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two…

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous…

We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…

This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…

Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…

We prove multiplicity theorems for Keller $ C_c^1 $-functionals on Frechet spaces and Finsler manifolds which are invariant under the action of a discrete subgroup. For such functionals, we evaluate the minimal number of critical points by…

The covariant two-point functions, derived from Ward identities in direct space, can be affected by consistency problems and can become unbounded for large time- or space-separations. This difficulty arises for several extensions of…

Liouville field theory is considered on domains with conformally invariant boundary conditions. We present an explicit expression for the three point function of boundary fields in terms of the fusion coefficients which determine the…

We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a…

Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…

We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of…

We investigate analyticity properties of correlation functions in conformal field theories (CFT) in the Wightman formulation. The goal is to determine domain of holomorphy of permuted Wightman functions. We focus on crossing property of…

We describe a class of theories obtained by fibering a Landau-Ginburg orbifold over a compact Kaehler base. While such theories are often described as phases of some GLSM, our description is independent of such an embedding. We provide a…

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal…

Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects,…