Hamiltonian formulation of Noncommutative D3--Brane

TL;DR

This paper develops a Hamiltonian framework for noncommutative D3-branes, revealing dualities and BPS bounds, and clarifies the role of space-time noncommutativity in gauge theories.

Contribution

It introduces a Hamiltonian formulation for noncommutative D3-branes that captures dualities without relying on Lagrangians, especially at first order in noncommutativity parameter.

Findings

Derived the Hamiltonian for space-time noncommutative D3-branes.

Established BPS bounds similar to ordinary D3-branes.

Connected noncommutative gauge theories with brane dynamics.

Abstract

Lagrangians of the Abelian Gauge Theory and its dual are related in terms of a shifted action. We show that in d=4 constrained Hamiltonian formulation of the shifted action yields Hamiltonian description of the dual theory, without referring to its Lagrangian. We apply this method, at the first order in the noncommutativity parameter theta, to the noncommutative U(1) gauge theory possessing spatial noncommutativity. Its dual theory is effectively a space--time noncommutative U(1) gauge theory. However, we obtain a Hamiltonian formulation where time is commuting. Space-time noncommutative D3--brane worldvolume Hamiltonian is derived as the dual of space noncommutative U(1) gauge theory. We show that a BPS like bound can be obtained and it is saturated for configurations which are the same with the ordinary D3-brane BIon and dyon solutions.