T-duality and background-dependence in genus corrections to effective actions

TL;DR

The paper shows that while the classical string effective action is background-independent, loop-level (genus) corrections introduce genuine background dependence due to winding modes in circle compactifications. It proposes a T-duality map that relates the loop-level D-dimensional theory at large radius (KK-dominated) to the base-space action at small radius (winding-dominated), revealing that the full loop-level action cannot be obtained by KK reduction of any covariant D-dimensional action. The analysis is carried out across bosonic, heterotic, and Type II theories, with explicit discussion of cosmological constants, Tr$(F^4)$ couplings, and moduli functions $h(oldsymbol{ ho})$ and $k(oldsymbol{ ho})$ constrained by S-duality in Type II. A key result is that dualities fix the asymptotic radius dependence of loop corrections while allowing genuinely stringy contributions that have no D-dimensional origin, highlighting the nuanced role of dualities in quantum corrections to effective actions.

Abstract

The classical effective action in string theory is background-independent, and its invariance under the Buscher rules constrains its form up to a few parameters. This work investigates how this picture changes at the quantum level, where loop corrections introduce an inherent background dependence. We propose a T-duality map for the loop-level effective action. It connects the circle-reduced effective action at large radius, where loops include only Kaluza-Klein (KK) momentum modes, to the base-space effective action at small radius, where loops include only winding modes. The resulting effective action is fundamentally distinct: it cannot be obtained from the KK reduction of any standard higher-dimensional action, revealing a uniquely stringy phenomenon at the loop level.