A Note on c=1 Virasoro Boundary States and Asymmetric Shift Orbifolds

TL;DR

This paper explores the construction of Virasoro boundary states in the c=1 free boson theory at arbitrary radii, revealing their properties and boundary entropy, especially at irrational radii, using asymmetric shift orbifolds and quotient algebra methods.

Contribution

It introduces a novel construction of Virasoro boundary states at generic radii via asymmetric shift orbifolds and analyzes their boundary entropy and algebraic structure.

Findings

Virasoro boundary states at irrational radius have infinite boundary entropy.

Boundary states are constructed using asymmetric shift orbifolds.

Non-fundamental boundary states' quotient algebra contains the noncommutative Weyl algebra.

Abstract

We comment on the conformal boundary states of the c=1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on the fundamental boundary states at the self-dual radius. We further calculate the boundary entropy and find that the Virasoro boundary states at irrational radius have infinite boundary entropy. The corresponding open string description of the asymmetric orbifold is given using the quotient algebra construction. Moreover, we find that the quotient algebra associated with a non-fundamental boundary state contains the noncommutative Weyl algebra.