arXiv subjects

Aonan Xu

Publications and source records attributed to Aonan Xu.

3 recordsLinked to original sources

arXiv2026

Bogomol'nyi Equations in Mixed Product Chern-Simons Theories Governing Charged Vortices and Antivortices

We extend product Chern-Simons theory to develop several mixed $U(1)\times U(1)$ models where one gauge field is governed by a Chern-Simons term and the other by a Maxwell or Born-Infeld term. We show that, by choosing suitable potentials, the energy functional admits a topological lower bound saturated by first-order self-dual equations. The resulting dyonic systems can be divided into vortex-vortex and vortex-antivortex configurations, and the coexistence of vortices and antivortices in the latter extends the vortex-only result known in product Chern-Simons model. On a doubly periodic domain, we establish Bradlow-type bounds with distinct physical implications: for vortex-only systems, the vortex numbers stay below this bound and cannot be arbitrarily large; for vortex-antivortex systems, the bound is imposed on the difference between the vortex and antivortex numbers, while the individual numbers are arbitrary. This distinction results in a bounded energy spectrum for the former and an unbounded energy spectrum for the latter.

hep-th↗

arXiv2026

Bogomol'nyi Equations in Two-Species Born--Infeld Theories Governing Vortices and Antivortices

We derive several new Bogomol'nyi (self-dual) equations in two-species $U(1)\times U(1)$ gauge theories governed by the Born--Infeld nonlinear electrodynamics. By identifying appropriate Born--Infeld type Higgs potentials, we show that the highly nonlinear energy functionals admit exact topological lower bounds saturated by coupled first-order equations. The resulting models accommodate both vortex-vortex and vortex-antivortex configurations and generalize previously known single-species Born--Infeld systems to interacting multi-component settings. Beyond the derivation of the Bogomol'nyi equations, we develop an exact thermodynamic theory for pinned multivortex configurations in both the full plane and compact doubly periodic domains. Owing to the linear dependence of the Bogomol'nyi energy spectrum on topological charges, we obtain closed-form expressions for the canonical partition function, internal energy, heat capacity, and magnetization. In compact domains, the Bradlow type geometric bounds constrain admissible vortex numbers and lead to qualitatively new high-temperature behavior. In particular, vortex-only systems exhibit spontaneous magnetization, while vortex-antivortex systems do not, reflecting the underlying symmetry between opposite topological charges. These results provide a rare analytically solvable framework for studying thermodynamics in nonlinear multi-component gauge theories regulated by the Born--Infeld electrodynamics.

hep-th↗

arXiv2025

Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in Generalized Abelian Higgs Theories

We derive the Bogomol'nyi equations in generalized Abelian Higgs theories which allow the coexistence of vortices and antivortices over a compact Riemann surface or the full plane. In the compact surface situation, we obtain a necessary and sufficient condition for the existence of a unique solution describing a system of coexisting vortices and antivortices. In the full-plane situation, we prove the existence of a unique solution representing an arbitrary distribution of vortices and antivortices and obtain sharp asymptotic behavior of the solution near infinity. These solutions carry quantized magnetic fluxes and energies explicitly expressed in terms of the numbers of vortices and antivortices topologically characterized by the first Chern and Thom classes.

math-ph↗