On the stability of Born-Infeld-regularised electroweak monopoles

Abstract: The Cho-Maison monopole provides a monopole solution of the electroweak field equations, but possesses an infinite classical energy due to the Maxwell form of the hypercharge sector. Motivated by string-inspired effective field theories, we study the perturbative stability of the Cho-Maison monopole when the hypercharge kinetic term is regularised by a Born-Infeld extension, which renders the monopole energy finite. Focusing on the bosonic electroweak theory with an unmodified $SU(2)_L$ sector and a Born-Infeld U(1)_Y sector, we analyze linear fluctuations about the regularised monopole background. Using a complex tetrad and a spin-weighted harmonic decomposition, we reduce the fluctuation equations to coupled radial Schroedinger-type eigenvalue problems and examine the spectrum of the resulting operators. We extend the separation-of-variables framework developed by Gervalle and Volkov to this non-linear gauge-field setting. We show that, after appropriate gauge fixing and constraint elimination, the Born-Infeld deformation preserves the angular channel structure of the Maxwell theory and leads to a self-adjoint Sturm-Liouville type problem for the stability of the radial modes, with modified radial coefficients determined by the background Born-Infeld profile. The resulting operator represents a smooth deformation of the Maxwell case and retains positive kinetic weight. Our results provide plausible evidence for the stability of the Born-Infeld deformed monopole and, most importantly, a systematic framework for future numerical or variational studies aimed at a definitive spectral analysis.