Tensionless spinning string: emergence of world-sheet torsion and covariant density of energy-momentum tensor

TL;DR

This paper investigates the properties of tensionless spinning strings, revealing the emergence of world-sheet torsion and analyzing the energy-momentum tensor's covariant divergence, highlighting differences from tensionful strings.

Contribution

It introduces a covariant energy-momentum tensor for tensionless spinning strings and demonstrates the emergence of world-sheet torsion, advancing understanding of their geometric and physical structure.

Findings

Covariant divergence of energy-momentum tensor vanishes due to bosonic-fermionic cancellation.

Emergence of world-sheet torsion in tensionless spinning strings.

Differences in worldsheet geometry between tensionless and tensionful strings analyzed.

Abstract

The action of tensionless spinning string invariant under reparametrizions, both local supersymmetry and dilatations, is considered. The density of energy-momentum tensor is constructed and vanishing of its covariant divergence is proved. This result arises from mutual cancellation of the bosonic and fermionic contributions. Differences in the geometry of worldsheets swept by tensionless and tensionfull spinning strings are analyzed. Shown is emergence of covariant trace of a torsion tensor on w-s of the tensionless spinning string. It is derived from the condition for the fermionic scalar density to be a composite one including the 2-dim. w-s density simulating the 4-dim. Rarita-Schwinger field. The said condition is accompanied with the Noether condition for covariant divergence of the vector metric density to vanish.