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. Focussing on the bosonic electroweak theory with an unmodified $$SU(2)_L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>L</mml:mi> </mml:msub> </mml:mrow> </mml:math> sector and a Born–Infeld $$U(1)_Y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>Y</mml:mi> </mml:msub> </mml:mrow> </mml:math> sector, we analyse 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 Schrödinger-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 nonlinear 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.