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Periods, coupling constants and modular functions in \(N=2\) SU(2) SYM with massive matter. (English) Zbl 0936.81043

Summary: We determine the mass dependence of the coupling constant for \(N = 2\) SYM with \(N_f = 1, 2, 3\) and 4 flavors. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to modular functions which enables us to give explicit formulas for the periods. Using the form of the \(J\)-functions we are able to determine in an elegant way the couplings and monodromies at the superconformal points.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
14H45 Special algebraic curves and curves of low genus
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
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