Magnetic impurities, integrable vortices and the Toda equation

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dc.contributor.author Gudnason, Sven Bjarke
dc.contributor.author Ross, Calum
dc.date.accessioned 2021-08-18T08:08:45Z
dc.date.available 2021-08-18T08:08:45Z
dc.date.issued 2021-07-21
dc.identifier.citation Gudnason, S.B., and Ross, C. (2021) 'Magnetic impurities, integrable vortices and the Toda equation', Letters in Mathematical Physics, 111, 100 (20pp). doi: 10.1007/s11005-021-01444-8 en
dc.identifier.volume 111 en
dc.identifier.startpage 1 en
dc.identifier.endpage 20 en
dc.identifier.issn 0377-9017
dc.identifier.uri http://hdl.handle.net/10468/11751
dc.identifier.doi 10.1007/s11005-021-01444-8 en
dc.description.abstract The five integrable vortex equations, recently studied by Manton, are generalized to include magnetic impurities of the Tong–Wong type. Under certain conditions, these generalizations remain integrable. We further set up a gauge theory with a product gauge group, two complex scalar fields and a general charge matrix. The second species of vortices, when frozen, are interpreted as the magnetic impurity for all five vortex equations. We then give a geometric compatibility condition, which enables us to remove the constant term in all the equations. This is similar to the reduction from the Taubes equation to the Liouville equation. We further find a family of charge matrices that turn the five vortex equations into either the Toda equation or the Toda equation with the opposite sign. We find exact analytic solutions in all cases and the solution with the opposite sign appears to be new. en
dc.description.sponsorship Henan University (Outstanding Talent Program) National Natural Science Foundation of China (Grant No. 11675223 and No. 12071111) en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Springer Nature Switzerland AG en
dc.rights © 2021, the Authors, under exclusive licence to Springer Nature B.V. This is a post-peer-review, pre-copyedit version of an article published in Letters in Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s11005-021-01444-8 en
dc.subject Vortex equations en
dc.subject Integrable vortices en
dc.subject Toda equation en
dc.subject Field theory on curved spaces en
dc.subject Impurities in field theory en
dc.title Magnetic impurities, integrable vortices and the Toda equation en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Calum Ross, Physics, University College Cork, Cork, Ireland. T: +353-21- 490-3000 E: calumross@ucc.ie en
dc.internal.availability Full text available en
dc.check.info Access to this article is restricted until 12 months after publication by request of the publisher. en
dc.check.date 2022-07-21
dc.description.version Accepted Version en
dc.contributor.funder Henan University en
dc.contributor.funder National Natural Science Foundation of China en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Letters in Mathematical Physics en
dc.internal.IRISemailaddress calumross@ucc.ie en
dc.identifier.articleid 100 en
dc.identifier.eissn 1573-0530


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