Orbifold boundary states from Cardy's condition

TL;DR

This paper constructs boundary states for D-branes at orbifold fixed points using Cardy's method, explores their interpretation, and generalizes to theories with discrete torsion, revealing new insights into fractional and wrapped branes.

Contribution

It introduces a systematic construction of boundary states for orbifold D-branes, including cases with discrete torsion, and clarifies their relation to fractional and wrapped branes.

Findings

Boundary states are explicitly constructed for orbifold fixed points.

The relation between fractional branes and wrapped branes is analyzed.

A new connection between discrete torsion phases and projective representations is established.

Abstract

Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardy's derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for $\mathbb{C}^2/\Gamma$ orbifolds. The boundary states are generalised to theories with discrete torsion and a new check is performed on the relation between discrete torsion phases and projective representations.