Effective action of bosonic string theory at order $\alpha'^3$

TL;DR

This paper derives the classical effective action of bosonic string theory at order 3, ensuring T-duality invariance and matching string scattering amplitudes, thus extending previous results to higher-derivative corrections.

Contribution

It provides the explicit form of the 3 order effective action for bosonic strings, fixing all couplings via T-duality and S-matrix matching, extending known lower-order results.

Findings

T-duality constrains all couplings at 3 order.

The derived action matches string S-matrix results.

The Riemann quartic terms agree with sigma-model calculations.

Abstract

In this work, we derive the classical effective action of bosonic string theory at order $\alpha'^{3}$ for the metric, Kalb-Ramond field, and dilaton by imposing a higher-derivative extension of the Buscher rules on the circular reduction of the minimal basis at this order, in the schemes where their corresponding actions at order $\alpha'$ are the Meissner and the Metsaev-Tseytlin schemes. We find that T-duality fixes all coupling constants in terms of the known overall factor at order $\alpha'$ and a single remaining parameter. This final parameter is determined by matching the single-trace term $\Tr(\epsilon \epsilon \epsilon \epsilon)$ in the four-graviton S-matrix element which lacks a massless pole, with the corresponding string theory amplitude. Our results for the Riemann quartic terms are in full agreement with those obtained from the nonlinear sigma-model approach.