Higher-derivative couplings in string theory: dualities and the B-field

TL;DR

The paper investigates the first quantum corrections to type II string theories at eight derivatives, focusing on how B-field couplings modify the classic $R^4$ terms. It proposes that replacing the curvature by the torsionful $R(\Omega_+)$ captures most B-field dependence in CP-even sectors, while odd-odd contributions require additional structures, notably involving $H^2R^3$ and $H^4R^2$ terms. The work provides complete five-point results, partial six-point results, and furnishes detailed tests via T-duality and heterotic/IIA duality, culminating in a proposed eleven-dimensional lift with $\hat{G}$-dependent terms. It also develops a six-dimensional duality framework to fix the structure of the corrections and discusses the ambiguities and lifts to higher dimensions, highlighting the role of generalized geometry in understanding higher-derivative couplings.

Abstract

The first quantum correction to the IIA string effective action arises at the eight-derivative level and takes the schematic form (t_8 t_8 - 1/8 εε)R^4 + B_2 \wedge X_8. This correction, however, cannot be complete by itself, as it is neither supersymmetric nor T-duality covariant. We reexamine these eight-derivative couplings and conjecture that the simple replacement R -> R(Ω_+), where Ω_+ = Ω+ 1/2 H is the connection with torsion, nearly completely captures their dependence on the B-field. The exception is in the odd-odd spin structure sector, where additional terms are needed. We present here a complete result at the level of the five-point function and a partial one for the six-point function. Further evidence for this conjecture comes from considering T-duality as well as heterotic/IIA duality beyond leading order. Finally, we discuss the eleven-dimensional lift of the modified one-loop type IIA couplings.