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The Glueball superpotential. (English) Zbl 1056.81054

Summary: We compute glueball superpotentials for four-dimensional, \({\mathcal N}=1\) supersymmetric gauge theories, with arbitrary gauge groups and massive matter representations. This is done by perturbatively integrating out massive charged fields. The Feynman diagram computations simplify, and are related to the corresponding matrix model. This leads to a natural notion of “projection to planar diagrams” for arbitrary gauge groups and representations. We discuss a general ambiguity in the glue-ball superpotential \(W(S)\) for terms, \(S^n\), whose order \(n\) is greater than the dual Coxeter number. This ambiguity can be resolved for all classical gauge groups \((A,B,C,D)\), via a natural embedding in an infinite rank supergroup. We use this to resolve some recently raised puzzles. For exceptional groups, we compute the superpotential terms for low powers of the glueball field and propose an all-order completion for some examples including \({\mathcal N}=1^*\) for all simply-laced groups. We also comment on compactification of these theories to lower dimensions.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
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