Non-renormalization theorems from extension to local coupling

TL;DR

This paper extends coupling constants to local fields to derive non-renormalization theorems in supersymmetric theories, revealing new anomalies and providing all-order beta function expressions.

Contribution

It introduces a method to derive non-renormalization theorems using local couplings, including the first all-order gauge beta function expression and anomaly analysis.

Findings

Non-renormalization of super-Yang-Mills beyond one-loop

Identification of a new supersymmetry anomaly at one-loop

All-order expression for the gauge beta function

Abstract

The extension of coupling constants to space-time dependent fields, the local couplings, makes possible to derive the non-renormalization theorems of supersymmetry by an algebraic characterization of Lagrangian N=1 supermultiplets. For super-Yang-Mills theories the construction implies non-renormalization of the coupling beyond one-loop order. However, renormalization in presence of the local gauge coupling is peculiar due to a new anomaly in one-loop order, which appears as an anomaly of supersymmetry in the Wess-Zumino gauge. As an application we derive the closed all-order expression for the gauge $\beta$ function and prove the non-renormalization of general N=2 supersymmetric theories from a cancellation of the susy anomaly.