Conformal perturbation theory beyond the leading order

TL;DR

This paper develops higher order conformal perturbation theory, providing explicit formulas for universal coefficients and analyzing boundary operator dimensions in specific geometric setups.

Contribution

It systematically identifies universal quantities in beta functions and derives explicit next-to-leading order formulas in terms of correlation functions.

Findings

Derived explicit formulas for universal coefficients at next-to-leading order.

Analyzed boundary operator dimensions for Neumann branes and intersecting branes.

Confirmed geometrical expectations in specific boundary configurations.

Abstract

Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients at next-to-leading order in terms of integrated correlation functions. As an example, we analyse the radius-dependence of the conformal dimension of some boundary operators for the case of a single Neumann brane on a circle, and for an intersecting brane configuration on a torus, reproducing in both cases the expected geometrical answer.