Higher-derivative corrections to type II supergravity:Four Ramond-Ramond terms

TL;DR

This paper calculates higher-derivative couplings of four Ramond-Ramond fields in type II supergravity, matching string theory results and exploring duality transformations to connect with known $ar{R}^4$ couplings.

Contribution

It explicitly derives eight-derivative couplings of four RR fields in supergravity and confirms them with string theory calculations, including effects of dualities.

Findings

Derived P-even and P-odd couplings of four RR fields.

Mapped P-even couplings to $ar{R}^4$ via T- and S-duality.

Confirmed couplings through direct string theory calculations.

Abstract

It is known that the sphere-level S-matrix element of four type II superstrings has one kinematic factor. At the low energy limit, this factor produces the kinematic factor of the corresponding Feynman amplitudes in the supergravity. It also produces higher-derivative couplings of four strings. In this paper, we explicitly calculate the kinematic factor of four RR states in the supergravity. Using this factor, we then find the eight-derivative P-even and P-odd couplings of four RR fields, including the self-dual RR five-form field strength. We show that the P-even couplings are mapped to the standard $\bar{R}^4$ couplings by linear T-duality and S-duality transformations. We also confirm the P-even couplings with direct calculations in type II superstring theories.