The Exact Effective Couplings of 4D N=2 gauge theories

Understand

The anomalous dimensions of operators in the purely gluonic SU(2,1|2) sector of any planar conformal N=2 theory can be read off from the N=4 SYM results by replacing the N=4 coupling constant by an interpolating function of the N=2 coupling constants, to which we refer to as the effective coupling.

• For a large class of N=2 theories we compute the weak coupling expansion of these functions as well as the leading strong coupling term by employing supersymmetric localization.
• Via Feynman diagrams, we interpret our results as the relative (between N=2 and N=4) finite renormalization of the coupling constant.
• Using the AdS/CFT dictionary, we identify the effective couplings with the effective string tensions of the corresponding gravity dual theories.