Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory

TL;DR

This paper investigates the structure of fixed points generated by exactly marginal operators in four-dimensional N=1 supersymmetric gauge theories, providing a unified method to identify these operators and exploring implications for dualities.

Contribution

It introduces a simple, unified prescription for identifying exactly marginal operators in N=1 supersymmetric gauge theories, extending to models with non-zero coupling and non-renormalizable theories.

Findings

Manifolds of fixed points are common in N=1 supersymmetric gauge theories.

The method can identify finite models with marginal operators at zero coupling.

Potential connections between N=1 duality and N=2 duality are proposed.

Abstract

We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N=1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N=2 supersymmetry. In particular we rely on the work of Shifman and Vainshtein relating the $\bt$-function of the gauge coupling to the anomalous dimensions of the matter fields. Finite N=1 models, which have marginal operators at zero coupling, are easily identified using our approach. The method can also be employed to find manifolds of fixed points which do not include the free theory; these are seen in certain models with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting implications. Using the fact that relevant perturbations often cause one manifold of fixed points to flow to another, we propose a specific mechanism through which the N=1 duality discovered by Seiberg could be associated with the duality of finite N=2 models.