D-branes in lens spaces

TL;DR

This paper constructs and analyzes boundary states and branes in lens space conformal field theories using algebraic methods, providing insights into fractional branes and symmetry breaking boundary conditions.

Contribution

It introduces an algebraic approach to study D-branes in lens spaces, enabling explicit computation of boundary states and boundary conditions.

Findings

Explicit boundary states for lens space CFTs

Analysis of fractional branes and symmetry breaking

Algebraic method simplifies understanding of boundary phenomena

Abstract

We realize the CFT with target a lens space SU(2)/Z_l as a simple current construction. This allows us to compute the boundary states and the annuli coefficients, and in particular to study the B-type branes, in purely algebraic terms. Several issues, like the appearance of fractional branes and symmetry breaking boundary conditions, can be addressed more directly in this approach than in a more geometric treatment.