D-branes in T-fold conformal field theory

TL;DR

This paper analyzes D-branes in T-fold conformal field theories, revealing geometric and non-geometric branes, their interactions, and how their physics may differ from traditional geometric backgrounds.

Contribution

It introduces a boundary CFT framework for T-folds, characterizes bulk and fractional D-branes, and explores their open string spectra and moduli dependence.

Findings

Bulk D-branes have geometric interpretations consistent with doubled torus formalism.

Fractional branes are non-geometric and lack geometric counterparts.

Open string modes exhibit non-linear moduli dependence, indicating non-geometric physics.

Abstract

We investigate boundary dynamics of orbifold conformal field theory involving T-duality twists. Such models typically appear in contexts of non-geometric string compactifications that are called monodrofolds or T-folds in recent literature. We use the framework of boundary conformal field theory to analyse the models from a microscopic world-sheet perspective. In these backgrounds there are two kinds of D-branes that are analogous to bulk and fractional branes in standard orbifold models. The bulk D-branes in T-folds allow intuitive geometrical interpretations and are consistent with the classical analysis based on the doubled torus formalism. The fractional branes, on the other hand, are `non-geometric' at any point in the moduli space and their geometric counterparts seem to be missing in the doubled torus analysis. We compute cylinder amplitudes between the bulk and fractional branes, and find that the lightest modes of the open string spectra show intriguing non-linear dependence on the moduli (location of the brane or value of the Wilson line), suggesting that the physics of T-folds, when D-branes are involved, could deviate from geometric backgrounds even at low energies. We also extend our analysis to the models with SU(2) WZW fibre at arbitrary levels.