Duality Symmetry of String Theory: A Worldsheet Perspective

TL;DR

This paper explores the duality and local symmetries of closed bosonic string theory using a worldsheet phase space approach, revealing duality covariant Ward identities and proposing T-duality symmetry for massive states.

Contribution

It demonstrates how to express local symmetries in a duality covariant form and proposes a new T-duality symmetry for massive string states, verified at the first massive level.

Findings

Ward identities can be expressed in a duality covariant form

An O(d,d) invariant Hamiltonian is constructed in toroidal compactification

Massive excited states exhibit T-duality symmetry, verified at the first level

Abstract

We study duality and local symmetries of closed bosonic string from the perspectives of worldsheet approach in the phase space path integral formalism. It is shown that the Ward identities reflecting the local symmetries associated with massless excitations such as graviton and antisymmetric tensor can be cast in a duality covariant form. It is shown how the manifestly O(d,d) invariant Hamiltonian can be obtained in the Hassan-Sen toroidal compactification scheme, d being the number of compact dimensions. It is proposed that massive excited states possess a T-duality symmetry for constant (tensor) backgrounds. This conjecture is verified for the first massive level.