Non-Abelian Duality in the String Effective Action

TL;DR

This paper investigates the symmetry properties of the string effective action under non-Abelian T-duality, showing proportionality between original and dual actions and establishing their equivalence in low-energy regimes.

Contribution

It demonstrates that the one-loop effective action remains proportional under non-Abelian T-duality, revealing a functional relation between Weyl anomaly coefficients.

Findings

Original and dual Lagrangians are proportional.

Reduced effective actions are equivalent.

Establishes a relation between Weyl anomaly coefficients.

Abstract

We study the symmetry of the one-loop effective action of bosonic string theory under non-Abelian T-duality transformations. It is shown that the original Lagrangian and its dual are proportional. This result implies that the corresponding reduced low energy effective actions are equivalent and leads to a functional relation between the Weyl anomaly coefficients of the original and dual two-dimensional non-linear sigma models. {}Finally, we apply this formalism to some simple examples.