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

TL;DR

This work analyzes the tensionless limit of a spinning string with local supersymmetry and dilatations, introducing worldsheet densities $\rho^{\mu}$, fermionic partners $\Sigma^{m}$, and a scale gauge field $a_{\mu}$. By formulating extended covariant derivatives and a composite fermionic density $\chi=\rho^{\mu}\chi_{\mu}$, the authors show that the worldsheet torsion reduces to its covariant trace $S_{\mu}$ in the tensionless regime, while the full torsion tensor remains underdetermined. They construct the energy-momentum tensor density $T^{\mu}{}_{\nu}$, prove its on-shell vanishing and tracelessness, and establish covariant conservation ${\bf D}_{\mu}T^{\mu}{}_{\nu}=0$ through exact boson–fermion cancellation. The results highlight a deep connection between tensionless (super)gauge dynamics and (super)gravity on the worldsheet, with potential implications for vacuum structure and holographic aspects of string theory. Overall, the paper clarifies how tensionless strings encode torsion and energy-momentum constraints within an extended dilatation–invariant framework.

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.