Domain walls with non-Abelian orientational moduli

TL;DR

This paper constructs and analyzes non-Abelian domain walls in U(N) gauge theories, exploring their moduli space, wave function behavior, and effective field theories, revealing how wall position moduli convert into orientational moduli as mass differences vanish.

Contribution

The paper introduces a detailed construction of non-Abelian domain walls, their moduli space, and effective theories, clarifying the transition of moduli types in gauge theories with degenerate Higgs masses.

Findings

Explicit form of the moduli space metric and Kahler potential.

Demonstration of wave function spreading of moduli between walls.

Clarification of the transition from position to orientational moduli.

Abstract

Domain walls with non-Abelian orientational moduli are constructed in U(N) gauge theories coupled to Higgs scalar fields with degenerate masses. The associated global symmetry is broken by the domain walls, resulting in the Nambu-Goldstone (and quasi-Nambu-Goldstone) bosons, which form the non-Abelian orientational moduli. As walls separate, the wave functions of the non-Abelian orientational moduli spread between domain walls. By taking the limit of Higgs mass differences to vanish, we clarify the convertion of wall position moduli into the non-Abelian orientational moduli. The moduli space metric and its Kahler potential of the effective field theory on the domain walls are constructed. We consider two models: a U(1) gauge theory with several charged Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental representation. More details are found in our paper published in Phys. Rev. D77 (2008) 125008 [arXiv:0802.3135 [hep-th]].