T-Duality and Two-Loop Renormalization Flows

TL;DR

This paper demonstrates the covariance of one-loop and two-loop renormalization group flows under T-duality in bosonic sigma models with abelian isometries, providing a strong consistency check for string theory backgrounds.

Contribution

It establishes T-duality covariance of renormalization flows at both one-loop and two-loop levels, extending previous results and testing the consistency of string backgrounds under duality transformations.

Findings

One-loop renormalization group flows are T-duality covariant.

Two-loop Weyl anomaly coefficients satisfy T-duality consistency conditions.

Provides a non-trivial test of T-duality covariance beyond effective action invariance.

Abstract

Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the target. For a restricted background, T-duality transformations are then studied at the next order, and the ensuing consistency conditions are found to be satisfied by the two-loop Weyl anomaly coefficients of the model. This represents an extremely non-trivial test of the covariance of renormalization group flows under T-duality, and a stronger condition than T-duality invariance of the string background effective action.