Target Space Duality as a Symmetry of String Field Theory

Toroidal backgrounds for bosonic strings are used to understand target spaceduality as a symmetry of string field theory and to study explicitly issues inbackground independence. Our starting point is the notion that the string fieldcoordinates $X(\sigma)$ and the momenta $P(\sigma)$ are background independentobjects whose field algebra is always the same; backgrounds correspond toinequivalent representations of this algebra. We propose classical string fieldsolutions relating any two toroidal backgrounds and discuss the space wherethese solutions are defined. String field theories formulated around dual backgrounds are shown to berelated by a homogeneous field redefinition, and are therefore equivalent, ifand only if their string field coupling constants are identical. Using thisdiscrete equivalence of backgrounds and the classical solutions we finddiscrete symmetry transformations of the string field leaving the string actioninvariant. These symmetries, which are spontaneously broken for genericbackgrounds, are shown to generate the full group of duality symmetries, and ingeneral are seen to arise from the string field gauge group.Comment: 72p