Are Genus Corrections in Effective Actions Invariant Under Buscher Rules?

TL;DR

This paper investigates whether genus corrections in string theory effective actions preserve Buscher symmetry, finding invariance only on self-dual circles and highlighting limitations of classical symmetry extensions at quantum levels.

Contribution

It extends the analysis of Buscher symmetry to higher-genus string world-sheets, revealing invariance constraints and limitations at quantum levels.

Findings

Invariance holds only on self-dual circles.

Higher-genus corrections break classical invariance.

Quantum effects prevent classical symmetry extension.

Abstract

It is well-established that the dimensional reduction of the classical effective action of string theory at any order of $\alpha'$ on a circle of arbitrary radius remains invariant under the higher-derivative extension of Buscher transformations. In this study, we extend this symmetry to higher-genus levels. By leveraging the validity of Buscher rules for any genus of the world-sheet, we find that the measure of the effective action remains invariant only when reduced on a self-dual circle. Our findings indicate that the invariance of the Lagrangian density under the higher-derivative and higher-genus extension of the corresponding restricted Buscher rules does not yield the one-loop effective action at order $\alpha'^3$ as derived by the S-matrix method. This result aligns with the general belief that quantum gravity has no global symmetry.