R^4, purified

TL;DR

This paper derives the complete four-point effective action for type II superstrings using the pure-spinor formalism, revealing a tensor product structure with superYang-Mills theory and including all fermionic contributions.

Contribution

It provides the full fermionic four-point effective action at all orders in 1, showing a novel tensor product structure with superYang-Mills theory and deriving the complete closed-string vertex operator.

Findings

Supergravity Lagrangian as tensor product of superYang-Mills Lagrangians.

Complete four-point effective action including fermions.

Derived all-order 1-expansion of the closed-string vertex operator.

Abstract

We derive, using the pure-spinor formalism, the complete -- including the fermions -- four-point effective action of both type II superstrings to all orders in $\alpha'$, at tree level in string loops. We find that, in the quartic-field approximation, the supergravity Lagrangian can be thought of as the tensor product, in a suitable sense, of two copies of the superYang-Mills Lagrangian in ten dimensions. The NS-NS three-form enters the supergravity Lagrangian through a modified connection with torsion. As a byproduct, we derive the complete, i.e. to all orders in the $\theta$-expansion, closed-string vertex operator in a flat target-space background.