Abstract
We present lattice Monte Carlo evidence of stable excitations of isolated static charges in the Higgs phase of the charge $q=2$ Abelian Higgs model. These localized excitations are excited states of the interacting fields surrounding the static charges. Since the $q=2$ Abelian Higgs model is a relativistic version of the Landau-Ginzburg effective action of a superconductor, we conjecture that excited states of this kind might be relevant in a condensed matter context. Taken together with recent related work in SU(3) gauge Higgs theory, our result suggests that a massive fermion excitation spectrum may be a general feature of gauge Higgs theories.
Highlights
Physical states in gauge field theories are gauge invariant, and this property implies that a static charge is necessarily accompanied by a surrounding field
We focus here on a simple Abelian gauge Higgs theory, namely the charge q 1⁄4 2 Abelian Higgs model, which is a relativistic generalization of the Landau-Ginzburg effective model of superconductivity
We have presented lattice Monte Carlo evidence for the existence of a stable excitation of the quantized fields surrounding isolated static charges, in the Higgs phase of the q 1⁄4 2 Abelian Higgs model in D 1⁄4 4 spacetime dimensions
Summary
Physical states in gauge field theories are gauge invariant, and this property implies that a static charge is necessarily accompanied by a surrounding field. This could be a Coulomb field extending to infinity, as in free field electrodynamics, or the charge of the state could be neutralized in some way by other charged dynamical fields. Greensite [6] has shown that there is a spectrum of localized excitations around an isolated fermion in SU(3) gauge Higgs theory, in the Higgs phase of the theory in four spacetime dimensions. In this article we will show that stable localized excitations of the massive photon and Higgs fields surrounding a static charge can exist in this theory, at least in some regions of the phase diagram. We believe this finding may be relevant to condensed matter systems, our present work is limited to this result in the relativistic model.
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