相关论文: On parity functions in conformal field theories

A brief heuristic explanation is given of recent work with Juergen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A…

We discuss some properties of the tower of mapping class group representations associated to a Rational Conformal Field Theory. In particular, after reviewing the elementary properties of the modular representation, we discuss the Galois…

Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…

This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the…

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 description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…

We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with…

We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…

In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie…

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.

We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.

For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…

We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.

We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the…

We classify the possible finite symmetries of conformal field theories with an affine Lie algebra su(2) and su(3), and discuss the results from the perspective of the graphs associated with the modular invariants. The highlights of the…

We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…