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

TL;DR

This paper investigates the eight-derivative quantum corrections in type IIA string theory, proposing a nearly complete B-field dependence via a modified Riemann tensor and supporting it with duality considerations and higher-point function calculations.

Contribution

It introduces a conjecture that replacing R with R(Ω_+) captures the B-field dependence in eight-derivative couplings, supported by explicit calculations and duality arguments.

Findings

Complete five-point function results for the couplings.

Partial six-point function results supporting the conjecture.

Evidence from T-duality and heterotic/IIA duality analyses.

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 \epsilon\epsilon)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(\Omega_+), where \Omega_+ = \Omega + 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.