BPS vortex from nonpolynomial scalar QED in a $\mathds{C}\mathrm{P}^1$-Maxwell theory

TL;DR

This paper explores vortex solutions in a generalized $ ext{CP}^1$-Maxwell theory with a field-dependent magnetic permeability induced by fermionic vacuum polarization, revealing novel BPS vortex configurations influenced by target-space geometry.

Contribution

It introduces a new non-polynomial magnetic permeability in a $ ext{CP}^1$-Maxwell model derived from fermionic effects, enabling the construction of BPS vortex solutions.

Findings

Derived a logarithmic magnetic permeability from fermionic vacuum polarization.

Constructed and solved BPS equations for vortex solutions.

Highlighted the influence of target-space geometry on vortex interactions.

Abstract

We investigate a generalized gauged $\mathds{C}\mathrm{P}^1$-Maxwell theory in which the electromagnetic sector acquires a field-dependent magnetic permeability generated dynamically through fermionic vacuum polarization. Starting from the gauged $\mathds{C}\mathrm{P}^1$-sigma model, whose dynamics occurs on a curved target space endowed with the Fubini-Study metric, we show that integrating out a Dirac fermion with effective mass induces, at one loop, a non-polynomial magnetic permeability, which after dimensional reduction to $(2+1)$-dimensions yields an effective Maxwell sector takes the form of a logarithmic magnetic permeability. Within this framework, one builds a generalized $\mathds{C}\mathrm{P}^1$-Maxwell model by admitting Bogomol'nyi-Prasad-Sommerfield (BPS) configurations. Taking this into account, we solved the self-dual equations that describe vortex-like solutions with quantized magnetic flux. Furthermore, one highlights the interactions between the target-space geometry and the induced permeability.