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Cordova, Clay Alexander

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Cordova

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Clay Alexander

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Cordova, Clay Alexander

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2011 - 20122

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Author's Publications: search.filters.isAuthorOfPublication.6cd33322-98dd-4d9c-8605-848c18f33c4f

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    Supersymmetric Spectroscopy
    (2012-08-17) Cordova, Clay Alexander; Vafa, C.
    We explore supersymmetric quantum field theories in three and four dimensions via an analysis of their BPS spectrum. In four dimensions, we develop the theory of BPS quivers which provides a simple picture of BPS states in terms of a set of building block atomic particles, and basic quantum mechanical interactions. We develop efficient techniques, rooted in an understanding of quantum-mechanical dualities, for determining the spectrum of bound states, and apply these techniques to calculate the spectrum in a wide class of field theories including ADE gauge theories with matter, and Argyres-Douglas type theories. Next, we explore the geometric content of quivers in the case when the four-dimensional field theory can be constructed from the six-dimensional (2; 0) superconformal field theory compactified on a Riemann surface. We find that the quiver and its superpotential are determined by an ideal triangulation of the associated Riemann surface. The significance of this triangulation is that it encodes the data of geodesics on the surface which in turn are the geometric realization of supersymmetric particles. Finally we describe a class of three-dimensional theories which are realized as supersymmetric domain walls in the previously studied four-dimensional theories. This leads to an understanding of quantum field theories constructed from the six-dimensional (2; 0) superconformal field theory compactified on a three-manifold, and we develop the associated geometric dictionary. We find that the structure of the field theory is determined by a decomposition of the three-manifold into tetrahedra and a braid which species the relationship between ultraviolet and infrared geometries. The phenomenon of BPS wall-crossing in four dimensions is then seen in these domain walls to be responsible for three-dimensional mirror symmetries.
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    T-Branes and Monodromy
    (Springer Verlag, 2011) Cecotti, Sergio; Cordova, Clay Alexander; Heckman, Jonathan; Vafa, Cumrun
    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.