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Global F-theory models: instantons and gauge dynamics. (English) Zbl 1214.81149
Summary: We present and analyze in detail a compact F-theory GUT model in which D-brane instantons generate the top Yukawa coupling non-perturbatively. We elucidate certain aspects of F-theory gauge dynamics which are absent in the Type IIB limit, due to quantum splitting of certain brane stacks. Finally, we provide a working implementation of an algorithm for computing cohomology of line bundles on arbitrary toric varieties. This should be of general use for studying the physics of global Type IIB and F-theory models, in particular for the explicit counting of zero modes for rigid F-theory instantons which contribute to charged matter couplings.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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