On Explicit Evaluations Around the Conformal Point in N=2 Supersymmetric Yang-Mills Theories

TL;DR

This paper derives explicit expressions for key quantities in N=2 supersymmetric Yang-Mills theories at the conformal point, using analytic continuation from weak coupling, and explores their relation to fixed points and SCFT.

Contribution

It provides explicit integral representations for periods and fields at the conformal point in various N=2 theories, clarifying their relation to beta functions and fixed points.

Findings

Explicit formulas for periods and Higgs fields at the conformal point.

Connection between fixed points in gauge theories and Landau-Ginzburg models.

Clarification of the relation to beta functions in different gauge groups.

Abstract

We show how to give the expression for periods, Higgs field and its dual of N=2 supersymmetric Yang-Mills theory around the conformal point. This is achieved by evaluating the integral representation in the weak coupling region, and by using analytic continuation to the conformal point. The explicit representation is shown for the SU(2) theory with matter fields and also for pure SU(N) and pure SO(2N) theory around the conformal point where the relation to the beta function of the theory is clarified. We also discuss a relation between the fixed points in the SU(2) theories with matter fields and the Landau-Ginzburg point of 2-D N=2 SCFT.