# Effective action of bosonic string theory at order $ \alpha'^2 $

## TL;DR

This paper determines the specific form of the bosonic string theory effective action at order α'^2 by fixing parameters through T-duality invariance, confirming consistency with S-matrix results.

## Contribution

It identifies the 60 parameters of the effective action at order α'^2 using T-duality invariance, aligning with previous S-matrix calculations.

## Key findings

- 60 parameters fixed by T-duality invariance
- Riemann cubed terms match S-matrix results
- Effective action consistent with gauge invariance

## Abstract

Recently, it has been shown that the gauge invariance requires the minimum number of independent couplings for $B$-field, metric and dilaton at order $\alpha'^2$ to be 60. In this paper we fix the corresponding 60 parameters in string theory by requiring the couplings to be invariant under the global T-duality transformations. The Riemann cubed terms are exactly the same as the couplings that have been found by the S-matrix calculations.