Duality and the Legendre Transform

TL;DR

This paper introduces a Legendre transform-based duality transformation for effective actions, extending the Seiberg-Witten duality in N=2 supersymmetric Yang-Mills theory to a broader context.

Contribution

It provides a new interpretation of duality as a Legendre transform of the effective action, applicable to various theories beyond supersymmetric Yang-Mills.

Findings

Legendre transform reproduces Seiberg-Witten duality

Generalizes duality to full effective actions

Applicable to other quantum field theories

Abstract

We define a weak-strong coupling transformation based on the Legendre transformation of the effective action. In the case of $N\es 2$ supersymmetric Yang-Mills theory, this coincides with the duality transform on the low energy effective action considered by Seiberg and Witten. This Legendre transform interpretation of duality generalizes directly to the full effective action, and in principle to other theories.