Periods, Coupling Constants and Modular Functions in N=2 SU(2) SYM with Massive Matter

Abstract

We determine the mass dependence of the coupling constant for N=2 SYM with N_f=1,2,3 and 4 flavours. 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.

Some changes, final version to appear in IJMPA. 14 LaTex pages

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• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2 Superconformal Field Theories
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• Four flavours, triality and bimodular forms
• Vacuum structure of spontaneously broken N=2 supersymmetric gauge theory
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
• Gluon condensates from the Hamiltonian formalism