Intersecting Solitons, Amoeba and Tropical Geometry

Simple item page
dc.creatorFujimori, Toshiaki
dc.creatorNitta, Muneto
dc.creatorOhta, Kazutoshi
dc.creatorSakai, Norisuke
dc.creatorYamazaki, Masahito
dc.date2008-05-08
dc.date.accessioned2026-07-07T11:50:38Z
dc.date.available2026-07-07T11:50:38Z
dc.descriptionWe study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin function. The general form of the Kahler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.
dc.description39 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/0805.1194
dc.identifierhttp://arxiv.org/abs/0805.1194
dc.identifierPhys.Rev.D78:105004,2008
dc.identifierdoi:10.1103/PhysRevD.78.105004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/203624
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.titleIntersecting Solitons, Amoeba and Tropical Geometry
dc.typetext

Files

Collections

arXiv