T-branes and monodromy

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.

6D supergravity without tensor multiplets

“…As mentioned above, further analysis of codimension 2 singularities in F-theory will be helpful in identifying which of the models found here have acceptable F-theory constructions. It has also recently been suggested that a more general class of brane constructions in F-theory may give rise to additional matter content from nonabelian structure in the Higgs field of the 7-brane world-volume theory [27]. It would be interesting to see if such constructions could give rise to some of the exotic matter representations encountered here for models with T = 0.…”

There and back again: a T-brane’s tale

“…Focusing (without loss of generality) on D7-branes, we explicitly show that the easiest possible T-brane configuration preserving minimal supersymmetry in 5 + 1 dimensions corresponds to a single D7-brane with vanishing worldvolume flux, extended along a specific holomorphic curve in the four remaining directions. 1 To reach our result we make a detour through a T-dual type IIA system consisting of D6-branes ending on a D8-brane, for which the relation between the non-Abelian [15] and the Abelian [16] description is well understood. Our T-brane tale is schematically depicted in figure 1: we start with the traditional description of T-branes via Hitchin-like equations for a stack of D7-branes, which relate the non-commuting worldvolume scalars to a non-trivial worldvolume flux.…”

“…Indeed, as explained in [1], the solution described above originates from the following constant nilpotent Higgs field in the so-called "holomorphic" gauge 7…”

The Tate form on steroids: resolution and higher codimension fibers

“…As observed already in [8] for SU(5), there are various choices for the small resolutions, which are all birationally equivalent. We shall find that the general structure of the geometries after resolving the codimension 1 singularities takes the form 19) where U, V depend on all sections (including the exceptional sections and the b n ). For SU(5), ℓ = 2 and the geometry is of a so-called binomial type, and was resolved by choosing the two loci for the small resolutions to be y = A = 0 and (y + V ) = B = 0 where A, B = ζ 1 , ζ 2 or U.…”