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On the quantum moduli space of vacua of \(N=2\) supersymmetric SU\((N_{c})\) gauge theories. (English) Zbl 0925.81347

Summary: We construct families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of \(N=2\) supersymmetric SU\((N_{c}\)) gauge theories coupled to \(N_{f}\) flavors of quarks in the fundamental representation. The quantum moduli spaces for \(N_{f} < N_{c}\) are determined completely by imposing \(R\)-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue and weak coupling monodromy calculations. The quantum moduli spaces for \(N_{f}\geqslant N_{c}\) theories are parameterized and their general structure is worked out using residue calculations. Global symmetry considerations suggest a complete description of them. The results are supported by weak coupling monodromy calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. We find an example of a novel symmetry of a quantum moduli space: Invariance under the exchange of a moduli parameter and the bare mass. We apply our method for the construction of the quantum moduli spaces of vacua of \(N=1\) supersymmetric theories in the Coulomb phase.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
14H99 Curves in algebraic geometry
81T13 Yang-Mills and other gauge theories in quantum field theory
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