g-function in perturbation theory

TL;DR

This paper verifies a gradient formula for boundary beta functions in 2D quantum field theory through explicit third-order perturbative calculations, including cases with resonant terms and divergences.

Contribution

It provides the first explicit third-order perturbative check of the gradient formula for boundary beta functions in open string field theory.

Findings

Gradient formula holds to third order in perturbation theory.

Resonant terms with logarithmic divergences are accommodated.

Universal nonlinearities in beta functions are identified.

Abstract

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disc. The form of the potential function and metric that we consider were introduced in hep-th/9210065, hep-th/9311177 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.