All-order generalized Green-Schwarz transformations

TL;DR

This work addresses constructing all-order generalized Green-Schwarz transformations (gGSt) compatible with $O(d,d)$ duality, enabling higher-derivative, duality-covariant corrections in string theory. It introduces the twisted Poláček-Siegel construction in a mega-space with the group $G_{ m PS}$, coupling it to a partial gauge-fixing strategy and torsion constraints to derive a remarkably simple all-order transformation law $\boxed{\delta E E^{-1} = - [A, D\xi_+] |_K}$ and to prove its closure with generalized diffeomorphisms. The resulting gauge algebra, including parameters $\Lambda_{21}$ and $\xi_{21}$, matches known Bergshoeff-de Roo-inspired results (gBdRi) at leading orders and reproduces the correct $α'^2$ corrections for bosonic and heterotic strings, while providing a practical all-order framework. The approach highlights how decoupling torsion constraints and a specific parameterization of the auxiliary field $oldsymbol{\mathcal{A}}$ can drastically simplify higher-derivative duality-covariant constructions, pointing to future extensions beyond the $O(d,d)$ subsector and exploring alternative torsion realizations.

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 $α'$-corrections to higher and higher orders, technically it becomes unfeasible beyond $α'^2$. 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.