Conformal quantum mechanics & the integrable spinning Fishnet
| Autor: | Enrico Olivucci, Sergey E. Derkachov |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Lattice Integrable Models Scalar (mathematics) FOS: Physical sciences Field Theories in Higher Dimensions Conformal map QC770-798 01 natural sciences Conformal group symbols.namesake Conformal symmetry Nuclear and particle physics. Atomic energy. Radioactivity 0103 physical sciences Feynman diagram 010306 general physics Mathematical physics Higher Spin Symmetry Physics Conformal Field Theory Nonlinear Sciences - Exactly Solvable and Integrable Systems 010308 nuclear & particles physics Conformal field theory Euclidean space Propagator High Energy Physics - Theory (hep-th) symbols Exactly Solvable and Integrable Systems (nlin.SI) |
| Zdroj: | Journal of High Energy Physics Journal of High Energy Physics, Vol 2021, Iss 11, Pp 1-30 (2021) |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/jhep11(2021)060 |
| Popis: | 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 $\Delta=2+i\nu$ for any left/right spins $\ell,\dot{\ell}$ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral \emph{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 $(\Delta_k,\ell_k, \dot{ \ell}_k)$ 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. 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 $\gamma$-deformed $\mathcal{N}=4$ and $\mathcal{N}=2$ supersymmetric theories. Comment: 25 pages, 28 figures; v2: (4.27) and Fig.16 improved, typos corrected; v3,v4: as re-submitted to JHEP; Figures added, typos corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink