Hamiltonian structure and noncommutativity in $p$-brane models with exotic supersymmetry

TL;DR

This paper derives the Hamiltonian for a super p-brane model with exotic supersymmetry, revealing noncommutative brackets and realizing the superalgebra without anomalies, advancing understanding of supersymmetric extended objects.

Contribution

It provides the Hamiltonian formulation, constraint analysis, and superalgebra realization for a super p-brane with partial supersymmetry preservation and noncommutative geometry.

Findings

Super p-brane Hamiltonian derived with preserved 3/4 supersymmetry.

Noncommutative Dirac brackets for super p-brane coordinates.

Realization of the OSp(1|8) superalgebra without anomalies.

Abstract

The Hamiltonian of the simplest super $p$-brane model preserving 3/4 of the D=4 N=1 supersymmetry in the centrally extended symplectic superspace is derived and its symmetries are described. The constraints of the model are covariantly separated into the first- and the second-class sets and the Dirac brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super $p$-brane coordinates and find the D.B. realization of the $OSp(1|8)$ superalgebra. Established is the coincidence of the D.B. and Poisson bracket realizations of the $OSp(1|8)$ superalgebra on the constraint surface and the absence there of anomaly terms in the commutation relations for the quantized generators of the superalgebra.