Clay Cordova

T-branes and monodromy

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.

Complex Chern-Simons from M5-branes on the Squashed Three-Sphere

A bstractWe derive an equivalence between the (2,0) superconformal M5-brane field theory dimensionally reduced on a squashed three-sphere, and Chern-Simons theory with complex gauge group. In the reduction, the massless fermions obtain an action which is second order in derivatives and are reinterpreted as ghosts for gauge fixing the emergent non-compact gauge symmetry. A squashing parameter in the geometry controls the imaginary part of the complex Chern-Simons level.

Schur Indices, BPS Particles, and Argyres-Douglas Theories

A bstractWe conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional N=2

Deformations of Superconformal Theories

\mathcal{N}=2

Infrared computations of defect Schur indices

field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify this conjecture for the special case of free field theories, N=2

Tangles, generalized Reidemeister moves, and three-dimensional mirror symmetry

\mathcal{N}=2