Boundary states for a free boson defined on finite geometries

TL;DR

This paper simplifies the construction of boundary states for a free boson on finite geometries, showing their explicit form and conformal invariance, which enhances understanding of boundary conditions in conformal field theory.

Contribution

The authors provide a more straightforward expression for boundary states of a free boson, removing technical assumptions and demonstrating their conformal invariance.

Findings

Explicit form of boundary states derived

Boundary states commute with boundary-preserving conformal transformations

Simplified construction aids in understanding boundary conditions

Abstract

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.