Moduli space coordinates and excited state g-functions

TL;DR

This paper explores the moduli space of boundary conditions in Virasoro minimal models, proposing that overlaps of bulk and boundary states serve as natural global coordinates, revealing the space's smooth and compact structure.

Contribution

It introduces a novel approach to parameterize the boundary condition space using overlaps derived from TBA descriptions, providing a global coordinate system.

Findings

Overlaps define a global coordinate on the boundary moduli space

The space of boundary conditions is shown to be smooth and compact

Explicit formulae for overlaps are derived from TBA data

Abstract

We consider the space of boundary conditions of Virasoro minimal models formed from the composition of a collection of flows generated by \phi_{1,3}. These have recently been shown to fall naturally into a sequence, each term having a coordinate on it in terms of a boundary parameter, but no global parameter has been proposed. Here we investigate the idea that the overlaps of particular bulk states with the boundary states give natural coordinates on the moduli space of boundary conditions. We find formulae for these overlaps using the known thermodynamic Bethe Ansatz descriptions of the ground and first excited state on the cylinder and show that they give a global coordinate on the space of boundary conditions, showing it is smooth and compact as expected.