Perturbative Beta Function of N=2 Super Yang-Mills Theories

TL;DR

This paper provides an algebraic proof that the perturbative beta function in N=2 Super Yang-Mills theories does not receive quantum corrections, based on a fundamental relationship involving gauge invariants and the scalar field.

Contribution

It offers a novel algebraic proof of the nonrenormalization theorem for the beta function in N=2 Super Yang-Mills theories, linking it to the vanishing anomalous dimension of a key gauge invariant.

Findings

Beta function remains unrenormalized at all perturbative orders.

The proof hinges on the vanishing anomalous dimension of Tr phi^2.

Establishes a fundamental relationship between the action and gauge invariants.

Abstract

An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N=2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N=2 Yang-Mills action and the local gauge invariant polynomial Tr phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.