The emergence of inherently 9-dimensional one-loop effective action from T-duality

TL;DR

This paper explores how T-duality in string theory leads to a nine-dimensional effective action with unique properties, revealing stringy couplings that cannot be simply lifted to ten dimensions.

Contribution

It explicitly computes and demonstrates the invariance of nine-dimensional couplings under T-duality and S-duality, highlighting their inherently stringy nature at order 3 in type IIA and IIB theories.

Findings

Derived nine-dimensional type IIB couplings invariant under S-duality.

Reproduced heterotic string couplings on T^5 from K3 reduction.

Identified stringy couplings that cannot be lifted to ten dimensions.

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 $\alpha'^3$ 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 \( T^5 \) at order \( \alpha' \), via the duality between the two theories.