$\mathbb{Z}_2$ boundary twist fields and the moduli space of D-branes

TL;DR

This paper develops a bosonized free field approach to boundary twist fields in conformal field theory, simplifying correlation function calculations and exploring D-brane moduli spaces.

Contribution

It introduces a bosonized representation of boundary twist fields, enabling easier computation of correlation functions and analysis of D-brane bound state deformations.

Findings

Simplified calculation of twist field correlation functions.

Access to higher order terms in operator product expansions.

Insights into the moduli space of D-brane bound states.

Abstract

We revisit the boundary conformal field theory of twist fields. Based on the equivalence between twisted bosons on a circle and the orbifold theory at the critical radius, we provide a bosonized representation of boundary twist fields and thus a free field representation of the latter. One advantage of this formulation is that it considerably simplifies the calculation of correlation functions involving twist fields. At the same time this also gives access to higher order terms in the operator product expansions of the latter which, in turn, allows to explore the moduli space of marginal deformation of bound states of D-branes. In the process we also generalize some results on correlation functions with excited twist fields.