Interpolating Action for Strings and Membranes - a Study of Symmetries in the Constrained Hamiltonian Approach

TL;DR

This paper develops a master action unifying string and membrane formalisms, analyzes their gauge symmetries via a constrained Hamiltonian approach, and explores implications for cosmological terms and connections to general relativity.

Contribution

It introduces a unified master action for strings and membranes, clarifies their gauge symmetries, and links membrane cosmological terms to Hamiltonian analysis.

Findings

Unified action interpolates between Nambu-Goto and Polyakov forms.

Differences between strings and membranes are linked to degrees of freedom.

Membrane cosmological term emerges naturally in the scheme.

Abstract

A master action for bosonic strings and membranes, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The role of the gauge symmetries vis-\`{a}-vis reparametrization symmetries of the various actions is analyzed by a constrained Hamiltonian approach. This analysis reveals the difference between strings and higher branes, which is essentially tied to a degree of freedom count. The cosmological term for membranes follows naturally in this scheme. The conncetion of our aproach with the Arnowitt--Deser--Misner representation in general relativity is illuminated.