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N=1 Geometries via M-theory

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arxiv 1307.7703 v2 pith:EIS6L5SA submitted 2013-07-29 hep-th

classification hep-th
keywords theoriesclassconfininggaugegeneralizedhitchinincludingm-theory
verification ladder T0 review T1 audit T2 compute T3 formal
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We provide an M-theory geometric set-up to describe four-dimensional N=1 gauge theories. This is realized by a generalization of Hitchin's equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin's system encode the infrared properties of the gauge theory in terms of N=1 curves. For N=1 deformations of N=2 theories in class S, we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases -- including Argyres-Douglas points, confining phases and gaugings of T_N theories -- and display new results for linear and generalized quivers.

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  1. Blowing-up the edge: connection formulae and stability chart of the Lam\'e equation

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    The paper derives the resummed Nekrasov-Shatashvili free energy from blow-up equations and uses it to compute the band-gap structure, connection formulas, and stability chart of the Lamé equation.

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