Gradient Flow in Logarithmic Conformal Field Theory

TL;DR

This paper investigates the gradient flow structure of beta-functions in logarithmic conformal field theories, relating them to a scalar function on moduli space and applying the findings to D-brane recoil in string theory.

Contribution

It establishes conditions for deriving worldsheet beta-functions as gradients of a scalar function in logarithmic CFTs and relates this to the Zamolodchikov C-function.

Findings

Beta-functions can be expressed as gradients of a scalar function.

A renormalization group invariant scalar function is derived.

Application to D-brane recoil demonstrates practical relevance.

Abstract

We establish conditions under which the worldsheet beta-functions of logarithmic conformal field theories can be derived as the gradient of some scalar function on the moduli space of running coupling constants. We derive a renormalization group invariant version of this function and relate it to the usual Zamolodchikov C-function expressed in terms of correlation functions of the worldsheet energy-momentum tensor. The results are applied to the example of D-brane recoil in string theory.