Conformal quantum mechanics & the integrable spinning Fishnet

Abstract In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile rep...

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Autores principales:	Sergey Derkachov, Enrico Olivucci
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Conformal Field Theory Field Theories in Higher Dimensions Higher Spin Symmetry Lattice Integrable Models Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/5f4e5510217c4ac885fe2945ae205e25
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spelling	oai:doaj.org-article:5f4e5510217c4ac885fe2945ae205e252021-11-14T12:41:01ZConformal quantum mechanics & the integrable spinning Fishnet10.1007/JHEP11(2021)0601029-8479https://doaj.org/article/5f4e5510217c4ac885fe2945ae205e252021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)060https://doaj.org/toc/1029-8479Abstract In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ, ℓ ̇ $$ \dot{\ell} $$ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆ k , ℓ k , ℓ ̇ $$ \dot{\ell} $$ k ) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed N $$ \mathcal{N} $$ = 4 and N $$ \mathcal{N} $$ = 2 supersymmetric theories.Sergey DerkachovEnrico OlivucciSpringerOpenarticleConformal Field TheoryField Theories in Higher DimensionsHigher Spin SymmetryLattice Integrable ModelsNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-30 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Conformal Field Theory Field Theories in Higher Dimensions Higher Spin Symmetry Lattice Integrable Models Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Conformal Field Theory Field Theories in Higher Dimensions Higher Spin Symmetry Lattice Integrable Models Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Sergey Derkachov Enrico Olivucci Conformal quantum mechanics & the integrable spinning Fishnet
description	Abstract In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ, ℓ ̇ $$ \dot{\ell} $$ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆ k , ℓ k , ℓ ̇ $$ \dot{\ell} $$ k ) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed N $$ \mathcal{N} $$ = 4 and N $$ \mathcal{N} $$ = 2 supersymmetric theories.
format	article
author	Sergey Derkachov Enrico Olivucci
author_facet	Sergey Derkachov Enrico Olivucci
author_sort	Sergey Derkachov
title	Conformal quantum mechanics & the integrable spinning Fishnet
title_short	Conformal quantum mechanics & the integrable spinning Fishnet
title_full	Conformal quantum mechanics & the integrable spinning Fishnet
title_fullStr	Conformal quantum mechanics & the integrable spinning Fishnet
title_full_unstemmed	Conformal quantum mechanics & the integrable spinning Fishnet
title_sort	conformal quantum mechanics & the integrable spinning fishnet
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/5f4e5510217c4ac885fe2945ae205e25
work_keys_str_mv	AT sergeyderkachov conformalquantummechanicstheintegrablespinningfishnet AT enricoolivucci conformalquantummechanicstheintegrablespinningfishnet
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Conformal quantum mechanics & the integrable spinning Fishnet

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