Explicitly connecting T and Buscher dualities in String Theory

TL;DR

This paper explicitly demonstrates how Buscher duality reduces to T-duality in string theory, using a pp-wave background as an example, and verifies the duality through Hamiltonian calculations.

Contribution

It provides a concrete example connecting Buscher duality to T-duality in a general background, specifically in a pp-wave setting, and verifies the duality explicitly.

Findings

Buscher duality reduces to T-duality in a pp-wave background.

Hamiltonians in both dual theories are explicitly computed and shown to be T-dual.

The study confirms the consistency of Buscher duality with T-duality beyond flat backgrounds.

Abstract

Buscher duality is a sigma-model duality, implemented by transformation of the target space. Not only in the case of a flat target space, but in a general background, should the Buscher duality reduce to the T-duality familiar in the flat-space string context. We exhibit this reduction explicitly using a pp-wave background as a tractable example. String theory is solved in a compactified Nappi-Witten background and the Buscher-dual theory is likewise solved. The Hamiltonian is computed in both cases, and the results are verified to be T-dual.