Bogomol'nyi equations for Kruglov strings
Abstract
We construct the Bogomol'nyi equations for Abelian gauge--Higgs vortices in which the Maxwell gauge sector is replaced by Kruglov nonlinear electrodynamics, a power-law family that interpolates between Maxwell theory, Born--Infeld electrodynamics, and exponential electrodynamics, characterized by a dimensionless exponent σ. Using the stressless method, we derive a pair of first-order equations directly from the vanishing of the spatial stress tensor, without assuming the Higgs potential \textit{a priori}. For generic σ, the gauge and Higgs sectors are coupled through an implicit algebraic relation. We therefore introduce a constitutive map Φ(Y;σ) and analyze its monotonicity and range to determine the conditions for a smooth admissible Bogomol'nyi branch. For σ>1/2, the constitutive map is strictly monotonic and unbounded, whereas for 0<σ<1/2 it possesses a finite maximum; the marginal case σ=1/2 is bounded. These properties yield explicit bounds on the nonlinear parameter β for the latter cases. We further obtain closed-form constitutive relations, BPS potentials, and gauge-field equations for six representative values of σ, spanning linear, quadratic, and cubic algebraic structures. The corresponding vortex profiles are then computed numerically. The resulting BPS string tension is purely topological, μBPS=2πn, independent of both σ and β.
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BibTeX
@misc{prasetyo2026bogomolnyi,
title = {{Bogomol'nyi equations for Kruglov strings}},
author = {I. Prasetyo and U. Ubaydillah and H. S. Ramadhan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08111},
eprint = {2609.08111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08111},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bogomol'nyi equations for Kruglov strings
AU - I. Prasetyo
AU - U. Ubaydillah
AU - H. S. Ramadhan
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2609.08111
UR - https://arxiv.org/abs/2609.08111
AB - We construct the Bogomol'nyi equations for Abelian gauge--Higgs vortices in which the Maxwell gauge sector is replaced by Kruglov nonlinear electrodynamics, a power-law family that interpolates between Maxwell theory, Born--Infeld electrodynamics, and exponential electrodynamics, characterized by a dimensionless exponent σ. Using the stressless method, we derive a pair of first-order equations directly from the vanishing of the spatial stress tensor, without assuming the Higgs potential \textit{a priori}. For generic σ, the gauge and Higgs sectors are coupled through an implicit algebraic relation. We therefore introduce a constitutive map Φ(Y;σ) and analyze its monotonicity and range to determine the conditions for a smooth admissible Bogomol'nyi branch. For σ>1/2, the constitutive map is strictly monotonic and unbounded, whereas for 0<σ<1/2 it possesses a finite maximum; the marginal case σ=1/2 is bounded. These properties yield explicit bounds on the nonlinear parameter β for the latter cases. We further obtain closed-form constitutive relations, BPS potentials, and gauge-field equations for six representative values of σ, spanning linear, quadratic, and cubic algebraic structures. The corresponding vortex profiles are then computed numerically. The resulting BPS string tension is purely topological, μ_BPS=2πn, independent of both σ and β.
ER -