Tensionless strings, correspondence with SO(D,D) sigma model

TL;DR

This paper establishes a correspondence between tensionless string theory with perimeter action and the SO(D,D) sigma model, revealing a geometric map that links these models and enables the construction of vertex operators similar to standard string theory.

Contribution

It demonstrates a linear transformation mapping tensionless strings to the SO(D,D) sigma model, clarifying their relationship and enabling vertex operator construction.

Findings

The perimeter action describes tensionless strings with a pure massless spectrum.

A linear transformation maps tensionless strings to the SO(D,D) sigma model with an Abelian constraint.

Vertex operators are constructed analogous to those in standard string theory.

Abstract

String theory with perimeter action is tensionless by its geometrical nature and has pure massless spectrum of higher spin gauge particles. I demonstrate that liner transformation of the world-sheet fields defines a map to the SO(D,D) sigma model equipped by additional Abelian constraint, which breaks SO(D,D) to a diagonal SO(1,D-1). The effective tension is equal to the square of the dimensional coupling constant of the perimeter action. This correspondence allows to view the perimeter action as a "square root" of the Nambu-Goto area action. The aforementioned map between tensionless strings and SO(D,D) sigma model allows to introduce the vertex operators in full analogy with the standard string theory and to confirm the form of the vertex operators introduced earlier.