Quantum energies of strings in a ()-dimensional gauge theory

Abstract

We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects.We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non-perturbative contribution to the total energy.

Quantum Corrections to Soliton Energies

“…So we are left with two angles ξ 1 and ξ 2 that parameterize the isospin orientation. 58 They will later be treated as variational parameters. For notational simplicity, we introduce the abbreviations s i = sin(ξ i ) and c i = cos(ξ i ).…”

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“…These topological defects are embedded NO vortices in the neutral Z µ massive vector field of electroweak theory, and the calculation may will be of experimental interest (even though some imaginary contribution to the energy will arise, because electroweak strings are unstable). In fact, there is an interesting paper on this subject, see [57], at the non-physical value of the weak angle equal to zero, and even a status report [58]. 7.…”

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