Equivalence of partition functions for noncommutative U(1) gauge theory and its dual in phase space

TL;DR

This paper demonstrates that noncommutative U(1) gauge theory and its dual have equivalent partition functions in phase space at first order in noncommutativity, using constrained Hamiltonian formalism and duality transformations.

Contribution

It extends the equivalence of partition functions to noncommutative gauge theories, establishing a connection between electric-magnetic and S-duality in this context.

Findings

Partition functions of noncommutative U(1) gauge theory and its dual are equivalent at first order in .

The approach applies constrained Hamiltonian formalism to relate dual theories.

Duality transformations invert strong and weak coupling regimes in noncommutative gauge theories.

Abstract

Equivalence of partition functions for U(1) gauge theory and its dual in appropriate phase spaces is established in terms of constrained hamiltonian formalism of their parent action. Relations between the electric--magnetic duality transformation and the (S) duality transformation which inverts the strong coupling domains to the weak coupling domains of noncommutative U(1) gauge theory are discussed in terms of the lagrangian and the hamiltonian densities. The approach presented for the commutative case is utilized to demonstrate that noncommutative U(1) gauge theory and its dual possess the same partition function in their phase spaces at the first order in the noncommutativity parameter \theta .