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arXiv · 2603.07803

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

F. C. E. Lima
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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.

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F. C. E. Lima. 2026-03-08. BPS vortex from nonpolynomial scalar QED in a $\mathds{C}\mathrm{P}^1$-Maxwell theory. https://arxiv.org/abs/2603.07803

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