Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory

TL;DR

This paper investigates the quantum stabilization of string configurations in a 2+1 dimensional gauge theory by calculating vacuum polarization energies from fermion fluctuations and exploring energy minimization through profile adjustments.

Contribution

It introduces a method to compute renormalized vacuum polarization energies in a 2+1D gauge theory and demonstrates how quantum effects can stabilize string configurations.

Findings

String configurations can bind many fermions.

Populating bound fermion levels lowers total energy.

Quantum effects may stabilize classical string solutions.

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.