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

TL;DR

This paper derives a unified analytic expression for the mass dependence of the coupling constant in N=2 SU(2) SYM with various flavors, using modular functions and Schwarzian triangle functions to analyze periods and monodromies.

Contribution

It provides a unified analytic framework for coupling constants in N=2 SYM with different flavors using modular and Schwarzian functions.

Findings

Unified expression for coupling constants across N_f=1,2,3,4

Explicit formulas for periods and monodromies at superconformal points

Connection between coupling constants and modular functions

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.