T-duality in Ramond-Ramond backgrounds

TL;DR

This work addresses the problem of T-duality in backgrounds with Ramond-Ramond and fermionic fields by employing the pure spinor worldsheet formalism to derive transformation rules for all target-space superfields. The authors gauge an isometry, perform a worldsheet path-integral analysis, and obtain classical Buscher-like rules for the NSNS sector along with fermionic transformations, including a parity-based redefinition to preserve the action form. They then establish quantum equivalence by regularizing the Gaussian integrations in a BRST-invariant manner, showing a dilaton shift $\\Phi' = \\\Phi - frac{1}{2} \\\ln G_{11}$ and proving non-perturbative in $l_s/R$ and all-orders-in-$g_s$ equivalence for arbitrary RR backgrounds. The approach provides a concise, general proof of T-duality that holds off-shell and on-shell, with potential applications to AdS$_5$ and other flux backgrounds, and suggests avenues for exploring global duality properties.

Abstract

Using the pure spinor formalism on the world-sheet, we derive the T-duality rules for all target space couplings in an efficient manner. The world-sheet path integral derivation is a proof of the equivalence of the T-dual Ramond-Ramond backgrounds which is valid non-perturbatively in the string length over the curvature radius and to all orders in perturbation theory in the string coupling.