Lagrange Multipliers and Couplings in Supersymmetric Field Theory

TL;DR

This paper explores the use of Lagrange multipliers as couplings in supersymmetric field theories, extending a-maximization to flow away from fixed points to better understand RG flow irreversibility.

Contribution

It demonstrates how to parametrize couplings so that Lagrange multipliers can be identified with actual couplings, impacting weakly coupled gauge theories.

Findings

Lagrange multipliers can be chosen as couplings in certain parametrizations.

Extension of a-maximization allows computation of anomalous dimensions along RG flows.

Insights into the irreversibility of RG flow in four-dimensional supersymmetric theories.

Abstract

In hep-th/0312098 it was argued that by extending the ``$a$-maximization'' of hep-th/0304128 away from fixed points of the renormalization group, one can compute the anomalous dimensions of chiral superfields along the flow, and obtain a better understanding of the irreversibility of RG flow in four dimensional supersymmetric field theory. According to this proposal, the role of the running couplings is played by certain Lagrange multipliers that are introduced in the construction. We show that one can choose a parametrization of the space of couplings in which the Lagrange multipliers can indeed be identified with the couplings, and discuss the consequences of this for weakly coupled gauge theory.