# Mass operator of the M2-brane on a background with constant three-form

## TL;DR

This paper derives the Hamiltonian of the supermembrane (M2-brane) in a specific background with a constant three-form field on a product space, advancing understanding of supermembrane dynamics in nontrivial backgrounds.

## Contribution

It provides the explicit formulation of the supermembrane Hamiltonian on a background with a constant three-form, extending previous models to more complex backgrounds.

## Key findings

- Hamiltonian of supermembrane on $M_9 imes T^2$ with constant three-form derived
- Enhanced understanding of supermembrane behavior in nontrivial backgrounds
- Framework for future studies of supermembrane interactions in complex geometries

## Abstract

The formulation of supermembrane theory on nontrivial backgrounds is discussed. In particular, we obtain the Hamiltonian of the supermembrane on a background with constant bosonic three form on a target space $M_9 \times T^2$.