Massive Stringy States and T-duality Symmetry

TL;DR

This paper provides evidence that T-duality symmetry extends to massive excited states in closed bosonic string theory, demonstrating an O(d,d) invariance for vertex operators across all massive levels.

Contribution

It introduces a systematic method to analyze T-duality symmetry of massive string states and shows that all such vertex operators can be expressed in an O(d,d) invariant form.

Findings

T-duality symmetry applies to massive string states.

Vertex operators can be formulated in an O(d,d) invariant manner.

Evidence verified for several massive levels.

Abstract

We present evidence for the target space duality symmetry associated with massive excited states of closed bosonic string. The evolution of string is considered in ${\hat D}$ spacetime dimensions; out of which d spacial dimensions are compactified on torus. The phase space Hamiltonian formulation is adopted to unveil the T-duality symmetry from the worldsheet perspective. The existence of this symmetry is verified for a few massive levels. A systematic procedure is presented to study T-duality symmetry of vertex operators for all massive levels of closed bosonic string. It is argued that all vertex operators corresponding to excited massive states can be cast in an O(d,d) invariant form where d is the number of compact dimensions.