Exceptional boundary states at c=1

TL;DR

The work addresses boundary conditions in a nonrational BCFT, focusing on a c=1 free boson at an irrational radius. It proposes an explicit Friedan boundary-state construction whose discrete Virasoro-sector coefficients are given by B_l(x) = P_l(x) with x in (-1,1), and demonstrates that these coefficients are uniquely fixed by the Cardy-Lewellen sewing constraints. The open-string channel spectrum is shown to be a continuous, nonnegative measure over Virasoro weights h, forming finite-width bands parameterized by geometric angles; at endpoints x = ±1 the states reduce to Dirichlet/Neumann mixtures. The results illuminate the structure of irrational BCFTs, reveal that these boundary states cannot be obtained by marginal deformations of a single standard boundary condition, and raise questions about Lagrangian realizations and D-brane interpretations in this context.

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.