On the vacuum states for noncommutative gauge theory

TL;DR

This paper investigates vacuum states in noncommutative gauge theories on Moyal spaces, demonstrating their invariance under certain symmetries and providing explicit configurations in two and four dimensions.

Contribution

It identifies and explicitly constructs invariant vacuum states in noncommutative gauge theories, highlighting their symmetry properties and providing concrete position-space expressions.

Findings

Vacuum states are invariant under global rotations and symplectic isomorphisms.

Explicit vacuum configurations are derived in two and four dimensions.

Supports the development of renormalisable gauge theories on noncommutative spaces.

Abstract

Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in the position space for these vacuum configurations in two and four dimensions.