Covariant canonical formalism for Dirac-Nambu-Goto bosonic p-branes and the Gauss-Bonnet topological term in string theory

TL;DR

This paper develops a covariant geometric framework for Dirac-Nambu-Goto p-branes and the Gauss-Bonnet topological term, identifying canonical variables and commutation relations in a curved background.

Contribution

It introduces a covariant, gauge-invariant formalism for analyzing p-branes and topological terms, providing new canonical variables and relations in string theory.

Findings

Identified canonical variables for p-branes in curved backgrounds

Established commutation relations for these variables

Derived canonical variables for the Gauss-Bonnet topological term

Abstract

Using a covariant and gauge invariant geometric structure constructed on the Witten covariant phase space for Dirac-Nambu-Goto bosonic p-branes propagating in a curved background, we find the canonically conjugate variables, and the relevant commutation relations are considered, as well as, we find the canonical variables for the Gauss-Bonnet topological term in string theory.