All-order generalized Green-Schwarz transformations

TL;DR

This paper introduces an all-order generalized Green-Schwarz transformation law in string theory, simplifying the computation of higher-derivative corrections and ensuring gauge algebra closure.

Contribution

It presents a new, simplified all-order transformation law for Green-Schwarz transformations, improving upon the generalized Bergshoeff-de Roo identification method.

Findings

The new transformation law is consistent with T-duality constraints.

Gauge algebra closure is explicitly verified.

The approach simplifies higher-order correction computations.

Abstract

Compatibility with T-duality severely constrains higher-derivative corrections to the low-energy supergravity limits of string theory. For example, it suggests that Lorentz transformations for heterotic strings are modified in precisely the way required for the Green-Schwarz anomaly cancellation mechanism. A systematic procedure to construct the resulting generalized Green-Schwarz transformations is the generalized Bergshoeff-de Roo identification (gBdRi). Although it in principle allows computing $\alpha'$-corrections to higher and higher orders, technically it becomes unfeasible beyond $\alpha'^2$. We revisit this problem with an alternative approach to the gBdRi, which we have recently developed. It gives rise to a very simple all-order transformation law whose closure we verify by explicitly computing the resulting gauge algebra.