Target Space Duality as a Symmetry of String Field Theory

TL;DR

This paper explores target space duality in string field theory, demonstrating that dual backgrounds are related by field redefinitions and identifying the symmetry transformations that generate duality groups.

Contribution

It introduces a classical solution framework relating dual toroidal backgrounds and shows how duality symmetries emerge from the string field gauge group.

Findings

Dual backgrounds are related by homogeneous field redefinitions.

Duality symmetries are generated by string field gauge transformations.

Background independence is characterized by the same field algebra across backgrounds.

Abstract

Toroidal backgrounds for bosonic strings are used to understand target space duality as a symmetry of string field theory and to study explicitly issues in background independence. Our starting point is the notion that the string field coordinates $X(\sigma)$ and the momenta $P(\sigma)$ are background independent objects whose field algebra is always the same; backgrounds correspond to inequivalent representations of this algebra. We propose classical string field solutions relating any two toroidal backgrounds and discuss the space where these solutions are defined. String field theories formulated around dual backgrounds are shown to be related by a homogeneous field redefinition, and are therefore equivalent, if and only if their string field coupling constants are identical. Using this discrete equivalence of backgrounds and the classical solutions we find discrete symmetry transformations of the string field leaving the string action invariant. These symmetries, which are spontaneously broken for generic backgrounds, are shown to generate the full group of duality symmetries, and in general are seen to arise from the string field gauge group.