https://doi.org/10.1140/epjc/s10052-026-15848-0
Regular Article - Theoretical Physics
The emergence of inherently 9-dimensional one-loop effective action from T-duality
Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad, Iran
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Received:
14
December
2025
Accepted:
14
May
2026
Published online:
3
June
2026
Abstract
Recent studies suggest that applying the Buscher rules to the dimensional reduction of ten-dimensional, one-loop effective actions generate “purely stringy” couplings in nine dimensions that cannot be lifted to a local, covariant form in ten dimensions. We investigate this phenomenon at order 
in type IIA string theory. By computing the circular reduction of the one-loop Chern–Simons term and pure-gravity couplings in type IIA theory and applying the T-duality transformation to the resulting couplings, we derive their counterparts in the type IIB effective action. We demonstrate that the resulting nine-dimensional type IIB couplings are invariant under S-duality without requiring contributions from the tree-level effective action or non-perturbative effects. As a consistency check, we show that the nine-dimensional type IIB couplings, when reduced on a K3 surface, reproduce the known heterotic string couplings on 
at order 
, via the duality between the two theories.
© The Author(s) 2026
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