String field theory, non-commutative Chern-Simons theory and Lie algebra cohomology

TL;DR

This paper constructs a class of noncommutative string field theories inspired by Chern-Simons theory, revealing classical solutions and observables without propagating open strings.

Contribution

It introduces a new class of string field theories with no open string degrees of freedom, expanding the understanding of noncommutative gauge theories.

Findings

Existence of non-trivial classical solutions

Presence of Wilson loop-like observables

Theories satisfy Witten's string field theory axioms

Abstract

Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We demonstrate the existence of non-trivial classical solutions. We find Wilson loop-like observables in these examples.