Bosonic Description of Spinning Strings in $2+1$ Dimensions

TL;DR

This paper develops a bosonic action principle for spinning strings in 2+1 dimensions, avoiding Grassmann variables, and extends the formulation to higher dimensions and other extended objects.

Contribution

It introduces a novel bosonic formulation of spinning strings using Poincare group variables, generalizable to higher dimensions and p-branes.

Findings

Provides a new action principle for spinning strings without Grassmann variables

Maintains standard string symmetries such as diffeomorphisms and Poincare invariance

Framework extends to membranes and p-branes in arbitrary dimensions

Abstract

We write down a general action principle for spinning strings in 2+1 dimensional space-time without introducing Grassmann variables. The action is written solely in terms of coordinates taking values in the 2+1 Poincare group, and it has the usual string symmetries, i.e. it is invariant under a) diffeomorphisms of the world sheet and b) Poincare transformations. The system can be generalized to an arbitrary number of space-time dimensions, and also to spinning membranes and p-branes.