Exceptional boundary states at c=1

TL;DR

This paper constructs and analyzes a new family of boundary states in a free boson CFT at irrational radius, revealing their conformal invariance and unique determination by sewing constraints, with a continuous spectrum in the open string channel.

Contribution

It explicitly constructs a novel 1-parameter family of boundary states breaking U(1) symmetry, extending the understanding of boundary conditions in irrational radius free boson CFTs.

Findings

Explicit construction of the boundary states.

States are uniquely determined by sewing constraints.

Open string spectrum is continuous with a nonnegative measure.

Abstract

We consider the CFT of a free boson compactified on a circle, such that the compactification radius $R$ is an irrational multiple of $R_{selfdual}$. Apart from the standard Dirichlet and Neumann boundary states, Friedan suggested [1] that an additional 1-parameter family of boundary states exists. These states break U(1) symmetry of the theory, but still preserve conformal invariance. In this paper we give an explicit construction of these states, show that they are uniquely determined by the Cardy-Lewellen sewing constraints, and we study the spectrum in the `open string channel', which is given here by a continous integral with a nonnegative measure on the space of conformal weights.