Gluing Branes, I

TL;DR

This paper explores the role of gluing morphisms in holomorphic brane configurations, detailing how to compute spectra and interactions with non-zero gluing VEVs, and discusses stability and metric approximation methods.

Contribution

It introduces rules for spectra and interactions with non-vanishing gluing VEVs and discusses stability criteria and metric approximation techniques for brane configurations.

Findings

Computed spectra and interactions with non-zero gluing VEVs.

Identified stability criteria for spectral data configurations.

Proposed a numerical method for hermitian-Einstein metric approximation.

Abstract

We consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are glued together, but is usually assumed to be vanishing. Here we explain the rules for computing spectra and interactions for configurations with non-vanishing gluing VEVs. We further give a detailed discussion of the D-terms for Higgs bundles, spectral covers and ALE fibrations. We highlight a stability criterion that applies to degenerate configurations of the spectral data, and address an apparent discrepancy between the field theory and ALE descriptions. This allows us to show that one gets walls of marginal stability in F-theory even though they are absent in the 11d supergravity description. We also propose a numerical approach for approximating the hermitian-Einstein metric of the Higgs bundle using balanced metrics.