TY - JOUR

T1 - Charged soliton of the three-dimensional CS+BI Abelian gauge theory

AU - Nastase, Horatiu

AU - Sonnenschein, Jacob

N1 - Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

PY - 2023/6/15

Y1 - 2023/6/15

N2 - In this paper, we construct a charged soliton with a finite energy and no delta function source in a pure Abelian gauge theory. Specifically, we first consider the three-dimensional Abelian gauge theory, with a Maxwell term and a level N CS term. We find a static solution that carries charge N, angular momentum N2 and whose radius is N independent. However, this solution has a divergent energy. In analogy to the replacement of the four-dimensional Maxwell action with the BI action, which renders the classical energy of a point charge finite, for the three-dimensional theory which includes a CS term such a replacement leads to a finite energy for the solution of above. We refer to this soliton as a CSBIon solution, representing a finite energy version of the fundamental (sourced) charged electron of Maxwell theory in four dimensions. In three dimensions the BI+CS action has a static charged solution with finite energy and no source, hence a soliton solution. The CSBIon, similar to its Maxwellian predecessor, has a charge N, angular momentum proportional to N and an N-independent radius. We also present other nonlinear modifications of Maxwell theory that admit similar solitons. The CSBIon may be relevant in various holographic scenarios. In particular, it may describe a D6-brane wrapping an S4 in a compactified D4-brane background. We believe that the CSBIon may play a role in condensed matter systems in 2+1 dimensions like graphene sheets.

AB - In this paper, we construct a charged soliton with a finite energy and no delta function source in a pure Abelian gauge theory. Specifically, we first consider the three-dimensional Abelian gauge theory, with a Maxwell term and a level N CS term. We find a static solution that carries charge N, angular momentum N2 and whose radius is N independent. However, this solution has a divergent energy. In analogy to the replacement of the four-dimensional Maxwell action with the BI action, which renders the classical energy of a point charge finite, for the three-dimensional theory which includes a CS term such a replacement leads to a finite energy for the solution of above. We refer to this soliton as a CSBIon solution, representing a finite energy version of the fundamental (sourced) charged electron of Maxwell theory in four dimensions. In three dimensions the BI+CS action has a static charged solution with finite energy and no source, hence a soliton solution. The CSBIon, similar to its Maxwellian predecessor, has a charge N, angular momentum proportional to N and an N-independent radius. We also present other nonlinear modifications of Maxwell theory that admit similar solitons. The CSBIon may be relevant in various holographic scenarios. In particular, it may describe a D6-brane wrapping an S4 in a compactified D4-brane background. We believe that the CSBIon may play a role in condensed matter systems in 2+1 dimensions like graphene sheets.

UR - http://www.scopus.com/inward/record.url?scp=85163775542&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.107.125011

DO - 10.1103/PhysRevD.107.125011

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AN - SCOPUS:85163775542

SN - 2470-0010

VL - 107

JO - Physical Review D

JF - Physical Review D

IS - 12

M1 - 125011

ER -