BPS lumps in the nonminimal $${\mathbb {C}}\textrm{P}^1$$ Maxwell–Chern–Simons model

Abstract We investigate self-dual radially symmetric configurations in the $${\mathbb {C}}\textrm{P}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mtext>P</mml:mtext> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> model coupled to a Maxwell and Chern–Simons (CS) gauge fields through of nonminimal interactions. Starting from the nonlinear O (3)-sigma model, we explicitly construct its classical mapping to the $${\mathbb {C}}\textrm{P}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mtext>P</mml:mtext> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> formulation, highlighting the emergence of a local U (1) gauge symmetry intrinsically associated with the Fubini–Study geometry of the target space. In the static regime, the combined effects of the Chern–Simons term and the Pauli-like nonminimal coupling modify the effective gauge connection, render the electric sector unavoidable, and give rise to magnetized and electrically polarized BPS lump configurations. By implementing the Bogomol’nyi procedure, we determine the self-interaction potential required for self-duality and derive the corresponding BPS equations. We show that the magnetic flux remains quantized and is completely fixed by the asymptotic behavior of the gauge field, even in the presence of the Chern–Simons and nonminimal couplings. A detailed asymptotic analysis further reveals that finite-energy solutions necessarily correspond to lump-like configurations in which the $${\mathbb {C}}\textrm{P}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mtext>P</mml:mtext> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> scalar field vanishes at spatial infinity. Numerical solutions of the BPS equations confirm that the resulting configurations are regular, spatially localized, and free of singularities, exhibiting confined magnetic flux together with a nontrivial localized electric field. These results show that the generalized $${\mathbb {C}}\textrm{P}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mtext>P</mml:mtext> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> -Maxwell-CS model supports self-dual solitons whose internal structure is rigidly governed by the target-space geometry rather than by spontaneous symmetry breaking.