Noncommutative Cohomological Field Theory and GMS soliton

TL;DR

This paper constructs a noncommutative cohomological field theory invariant under shifts in the noncommutative parameter, demonstrating its partition function equals the Euler number of GMS soliton space, linking quantum field theory and soliton topology.

Contribution

It introduces a novel noncommutative cohomological field theory invariant under parameter translation, and computes its partition function as the Euler number of GMS soliton space.

Findings

Partition function equals the Euler number of GMS soliton space.

Constructed a noncommutative cohomological scalar field theory.

Demonstrated invariance under noncommutative parameter translation.

Abstract

We show that it is possible to construct a quantum field theory that is invariant under the translation of the noncommutative parameter $\theta_{\mu\nu}$. This is realized in a noncommutative cohomological field theory. As an example, a noncommutative cohomological scalar field theory is constructed, and its partition function is calculated. The partition function is the Euler number of Gopakumar, Minwalla and Strominger (GMS) soliton space.