Two-Loop Beta Functions Without Feynman Diagrams

TL;DR

This paper derives the two-loop beta functions for a bosonic sigma model using symmetry principles rather than Feynman diagrams, highlighting the constraining power of T-duality on renormalization.

Contribution

It presents a novel method to compute two-loop beta functions without Feynman diagrams, based on T-duality symmetry and renormalization group consistency.

Findings

Two-loop beta functions are obtained without Feynman diagrams.

T-duality symmetry constrains renormalization flows significantly.

The method applies to generic torsionless backgrounds.

Abstract

Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained without Feynman diagram calculations, and represents further evidence that duality symmetry severely constrains renormalization flows.