The space of local operators in perturbed conformal field theories,

TL;DR

This paper investigates the structure of local operators in massive deformations of conformal field theories, revealing a correspondence with the original conformal theory and exploring solutions related to para-fermionic operators.

Contribution

It demonstrates the existence of chiral sectors in deformed theories and characterizes the full operator space, including para-fermionic solutions, using q-series and Rogers-Ramanujan identities.

Findings

Chiral sectors mirror the original conformal theory

Operator space includes descendent spaces of scalar fields

Solutions for para-fermionic operators are identified

Abstract

The space of local operators in massive deformations of conformal field theories is analysed. For several model systems it is shown that one can define chiral sectors in the theory, such that the chiral field content is in a one-to-one correspondence with that of the underlying conformal field theory. The full space of operators consists of the descendent spaces of all scalar fields. If the theory contains asymptotic states which satisfy generalised statistics, the form factor equations admit in addition also solutions corresponding to the descendent spaces of the para-fermionic operators of the same spin as the asymptotic states. The derivation of these results uses $q$-sum expressions for the characters and $q$-difference equations used in proving Rogers-Ramanujan type identities.