# Noncommutative gauge theories on D-branes in non-geometric backgrounds

## TL;DR

This paper explores noncommutative gauge theories on D-branes in non-geometric backgrounds derived from T-duality, revealing new classes of noncommutative fibrations and the role of dual coordinates in R-flux backgrounds.

## Contribution

It provides a detailed analysis of D-branes in non-geometric backgrounds, including Morita duality monodromies and new examples of noncommutative fibrations with non-geometric fibers.

## Key findings

- T-duality induces Morita duality monodromies in noncommutative gauge theories.
- Parabolic twists recover known noncommutative torus bundles; elliptic twists produce new fibrations.
- Backgrounds with R-flux depend explicitly on dual coordinates, lacking conventional spacetime description.

## Abstract

We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional T-folds, examining both cases of parabolic and elliptic twists in detail. We give a detailed description of the decoupling limits and explore various physical consequences of the open string non-geometry. The T-duality monodromies of the non-geometric backgrounds lead to Morita duality monodromies of the noncommutative Yang-Mills theories induced on the D-branes. While the parabolic twists recover the well-known examples of noncommutative principal torus bundles from topological T-duality, the elliptic twists give new examples of noncommutative fibrations with non-geometric torus fibres. We extend these considerations to D-branes in backgrounds with R-flux, using the doubled geometry formulation, finding that both the non-geometric background and the D-brane gauge theory necessarily have explicit dependence on the dual coordinates, and so have no conventional formulation in spacetime.