Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory

Abstract An infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4...

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Autor principal:	Fabrizio Canfora
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/9d0e0feca53d45138c95fa45a0cc4cee
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spelling	oai:doaj.org-article:9d0e0feca53d45138c95fa45a0cc4cee2021-11-28T12:11:42ZNon-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory10.1140/epjc/s10052-021-09837-81434-60441434-6052https://doaj.org/article/9d0e0feca53d45138c95fa45a0cc4cee2021-11-01T00:00:00Zhttps://doi.org/10.1140/epjc/s10052-021-09837-8https://doaj.org/toc/1434-6044https://doaj.org/toc/1434-6052Abstract An infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).Fabrizio CanforaSpringerOpenarticleAstrophysicsQB460-466Nuclear and particle physics. Atomic energy. RadioactivityQC770-798ENEuropean Physical Journal C: Particles and Fields, Vol 81, Iss 11, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Fabrizio Canfora Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
description	Abstract An infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).
format	article
author	Fabrizio Canfora
author_facet	Fabrizio Canfora
author_sort	Fabrizio Canfora
title	Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
title_short	Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
title_full	Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
title_fullStr	Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
title_full_unstemmed	Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory
title_sort	non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional yang–mills theory
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/9d0e0feca53d45138c95fa45a0cc4cee
work_keys_str_mv	AT fabriziocanfora nonlinearcompositionandinfiniteconformalsymmetryoftopologicallynontrivialsolutionsin3131dimensionalyangmillstheory
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Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$ ( 3 + 1 ) -dimensional Yang–Mills theory

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