Tensionless strings and the space-time signature change

TL;DR

This paper develops a tensionless string model in a (2,2) signature space-time, revealing how signature change affects the holonomy group and enabling the construction of a worldsheet Dirac operator, unlike in standard Minkowski space.

Contribution

It introduces a tensionless string model in a (2,2) signature space-time and demonstrates the impact of signature change on the holonomy group and Dirac operator formulation.

Findings

Signature change alters the holonomy group structure.

A worldsheet Dirac operator invariant under the holonomy group is possible in (2,2) space.

Such a Dirac operator cannot be constructed in (3+1)-dimensional Minkowski space.

Abstract

We construct a tensionless string model in a four-dimensional space-time ${\bf R}^{2,2}$ with the (2,2) signature and solve the string equations. We find that the signature change radically changes the structure of the holonomy group of the null worldsheet. As a result the introduction of the worldsheet Dirac operator invariant under the holonomy group becomes possible. We show that the such possibility is absent in the tensionless string model in the (3+1)-dimensional Minkowski space.