Multivalued Fields on the Complex Plane and Conformal Field Theories

TL;DR

This paper explores a class of conformal field theories with nonabelian and discrete symmetries, realized through free scalar fields and algebraic curves, with explicit solutions to Knizhnik-Zamolodchikov equations, revealing novel operator statistics and connections to curved space-times.

Contribution

It introduces a new class of conformal field theories with nonstandard statistics, explicitly solves their conformal blocks, and investigates their relation to curved space-times in two dimensions.

Findings

Explicit solutions to Knizhnik-Zamolodchikov equations for these theories

Operators obey nonstandard statistics in the constructed models

Connections between operator statistics and curved space-times in 2D

Abstract

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides of the fact that one obtains in this way an entire class of theories in which the operators obey a nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.