Deviations from Scale Invariance near a General Conformal Background

TL;DR

This paper investigates how small perturbations affect scale invariance in two-dimensional conformal field theories by analyzing beta functions for various couplings, providing a general perturbative framework without specific assumptions.

Contribution

It offers a perturbative expression for beta functions in general 2D conformal field theories under local scale changes, including couplings to primary operators, descendants, and dilatonic terms.

Findings

Beta functions are expressed perturbatively in terms of original conformal data.

The analysis includes couplings to primary operators, descendants, and curvature-dependent terms.

Provides a general framework applicable to various 2D conformal theories.

Abstract

Deviations from scale invariance resulting from small perturbations of a general two dimensional conformal field theory are studied. They are expressed in terms of beta functions for renormalization of general couplings under local change of scale. The beta functions for homogeneous background are given perturbatively in terms of the data of the original conformal theory without any specific assumptions on its nature. The renormalization of couplings to primary operators and to first descendents is considered as well as that of couplings of a dilatonic type which involve explicit dependence on world sheet curvature.