Resolution of Overlapping Branes

TL;DR

This paper presents methods to resolve singularities in overlapping brane configurations by replacing transverse spaces with Eguchi-Hanson or Taub-NUT geometries, leading to regular supergravity solutions relevant for supersymmetric gauge theories.

Contribution

It introduces a novel approach to singularity resolution in overlapping branes using special geometries, maintaining T-duality and providing regular supergravity duals.

Findings

Resolved 5-branes and D4-branes are constructed with regular geometries.

The solutions preserve T-duality invariance after resolution.

These configurations serve as smooth supergravity duals of supersymmetric Yang-Mills theories.

Abstract

We obtain singularity resolutions for various overlapping brane configurations, including those of two heterotic 5-branes, type II 5-branes or D4-branes. In these solutions, the ``harmonic'' function H for each brane component depends only on the associated four-dimensional relative transverse space. The resolution is achieved by replacing these transverse spaces with Eguchi-Hanson or Taub-NUT spaces, both of which admit a normalisable self-dual (or anti-self-dual) harmonic 2-form. Due to the manner in which the interaction terms for the form fields modify their Bianchi identities or equations of motion, these normalisable harmonic 2-forms provide regular sources for the branes. We also obtain resolved 5-branes and D4-branes wrapped on S^1, which is fibred over the transverse Eguchi-Hanson or Taub-NUT spaces. The T-duality invariance of the NS-NS 5-brane is retained after the resolution. The resolved 5-branes and D4-branes provide regular supergravity duals of certain supersymmetric Yang-Mills theories in five and four dimensions.