# T-branes and defects

## TL;DR

This paper investigates T-branes on compact Kaehler surfaces with localized defect fields, revealing how defect sources relax constraints on T-brane configurations and connect to Hitchin systems with defects.

## Contribution

It demonstrates how defect-localized fields modify T-brane profiles, relax global constraints, and relate to Hitchin systems with defects, providing new insights into their geometric and physical structure.

## Key findings

- Defect sources induce pole profiles in T-branes.
- Relaxation of constraints allows T-branes on positively curved surfaces.
- Connection established between Hitchin systems with defects and global symmetry enhancements.

## Abstract

We study T-branes on compact Kaehler surfaces, in the presence of fields localised at curves. If such fields are treated as defects, their vevs induce delta-function sources for the 7-brane background, possibly leading to profiles with poles. We find that the presence of defect sources relaxes the constraints on globally well-defined T-brane configurations, avoiding the obstruction to building them on surfaces of positive curvature. Profiles with poles can be understood, from a 4d viewpoint, as non-trivial vevs for massive modes induced by the defects, and come with their own set of constraints. In the special case of fields localised on a self-intersection curve, we show how to retrieve the Hitchin system with defects from an ordinary global one with enhanced symmetry.