https://doi.org/10.1140/epjc/s10052-025-14060-w
Letter
Are genus corrections in effective actions invariant under Buscher rules?
Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad, Iran
Received:
23
December
2024
Accepted:
11
March
2025
Published online:
19
March
2025
It is well-established that the dimensional reduction of the classical effective action of string theory at any order of 
on a circle of arbitrary radius remains invariant under the higher-derivative extension of Buscher transformations. In this study, we investigate the extension of 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 
as derived by the S-matrix method. This result aligns with the general belief that quantum gravity has no global symmetry.
© The Author(s) 2025
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