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

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.