Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

TL;DR

This paper investigates domain wall solitons in noncommutative field theories with Hopf algebraic translational symmetries, demonstrating their existence, explicit solutions, and associated massless moduli fields in a specific Lie-algebraic noncommutative spacetime.

Contribution

It introduces the first explicit construction of domain wall solitons in braided noncommutative field theories with Hopf algebraic translational symmetry and analyzes their properties.

Findings

Existence of domain wall solitons in noncommutative field theories.

Explicit one-parameter family of solutions perturbative in noncommutativity.

Identification of massless moduli fields propagating on the solitons.

Abstract

Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar phi^4 braided noncommutative field theory in Lie-algebraic noncommutative spacetime, [x^i,x^j]=2i kappa epsilon^{ijk}x_k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter kappa. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry.