Noncommutative Solitons

TL;DR

This paper constructs classically stable noncommutative solitons, including instantons and vacuum bubbles, in scalar and gauge theories, revealing how noncommutativity influences their stability and structure.

Contribution

It introduces a method to find stable solitons in noncommutative scalar and gauge theories using operator correspondence, highlighting new solution structures.

Findings

Stable instantons and vacuum bubbles are found in noncommutative scalar theories.

Noncommutativity sets the size of the solitons by the noncommutative scale.

Expanding around simple solutions simplifies the gauge theory action.

Abstract

We find classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative field theories whose scalar potential, $V(\ph)$, has at least two minima. These solutions are bubbles of the false vacuum whose size is set by the scale of noncommutativity. Our construction uses the correspondence between non-commutative fields and operators on a single particle Hilbert space. In the case of noncommutative gauge theories we note that expanding around a simple solution shifts away the kinetic term and results in a purely quartic action with linearly realised gauge symmetries.