T-Branes and Monodromy

TL;DR

T-branes are a new class of non-abelian brane bound states with upper triangular Higgs fields, refining monodromic branes in F-theory, and enabling new phenomenological and theoretical insights.

Contribution

The paper introduces T-branes, a novel non-abelian brane configuration, and demonstrates their implications for localized matter, Yukawa couplings, and constraints in F-theory GUT models.

Findings

T-branes allow localized matter on complex codimension one subspaces.

Yukawa couplings can be computed for T-branes and are localized in codimension two.

Eigenvalues of the Higgs field may not fully determine the spectrum of localized modes.

Abstract

We introduce T-branes, or "triangular branes," which are novel non-abelian bound states of branes characterized by the condition that on some loci, their matrix of normal deformations, or Higgs field, is upper triangular. These configurations refine the notion of monodromic branes which have recently played a key role in F-theory phenomenology. We show how localized matter living on complex codimension one subspaces emerge, and explain how to compute their Yukawa couplings, which are localized in complex codimension two. Not only do T-branes clarify what is meant by brane monodromy, they also open up a vast array of new possibilities both for phenomenological constructions and for purely theoretical applications. We show that for a general T-brane, the eigenvalues of the Higgs field can fail to capture the spectrum of localized modes. In particular, this provides a method for evading some constraints on F-theory GUTs which have assumed that the spectral equation for the Higgs field completely determines a local model.