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Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-Theory

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Abstract

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in F-theory, to study non-abelian gauge symmetry. Since this branch of the moduli space also exists in the defining M-theory compactification, it provides the only known description of gauge theory states that exists in both pictures; they are string junctions in F-theory. We discuss how global deformations give rise to local deformations, and also give examples where local deformation can be utilized even in models where a global deformation does not exist. Utilizing deformations, we study a number of new examples, including non-perturbative descriptions of SU(3) and SU(2) gauge theories on seven-branes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these non-perturbative descriptions do not exist for higher rank SU(N) theories.

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  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    Antonella Grassi & Julius L. Shaneson

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, USA

    James Halverson

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  1. Antonella Grassi
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  2. James Halverson
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Correspondence to James Halverson.

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Grassi, A., Halverson, J. & Shaneson, J.L. Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-Theory. Commun. Math. Phys. 336, 1231–1257 (2015). https://doi.org/10.1007/s00220-015-2313-0

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