Abelian duality, walls and boundary conditions in diverse dimensions

TL;DR

This paper explores the application of duality walls to understand how duality transformations affect boundary conditions and operators across various dimensions, revealing geometric insights into T-duality and D-branes.

Contribution

It introduces a systematic formalism for duality walls in multiple dimensions and characterizes T-duality actions on D-branes using differential geometry and Fourier-Mukai transforms.

Findings

Constructed a large class of D-branes for 2D sigma-models with toroidal targets.

Determined the action of T-duality group on D-branes.

Showed T-duality acts as a Fourier-Mukai transform in this formalism.

Abstract

We systematically apply the formalism of duality walls to study the action of duality transformations on boundary conditions and local and nonlocal operators in two, three, and four-dimensional free field theories. In particular, we construct a large class of D-branes for two-dimensional sigma-models with toroidal targets and determine the action of the T-duality group on it. It is manifest in this formalism that T-duality transformations on D-branes are given by a differential-geometric version of the Fourier-Mukai transform.