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Hexagonalization of Fishnet integrals I: mirror excitations
TLDR
In this paper, a conformal invariant chain of sites in the unitary irreducible representations of the group is considered and its spectrum and eigenfunctions are obtained by separation of variables.Abstract:
In this paper we consider a conformal invariant chain of $L$ sites in the unitary irreducible representations of the group $SO(1,5)$. The $k$-th site of the chain is defined by a scaling dimension $\Delta_k$ and spin numbers $\frac{\ell_k}{2}$, $\frac{\dot{\ell}_k}{2}$. The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice "fishnet" integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the $\textit{mirror excitations}$ of the lattice: particles with $SO(4)$ internal symmetry that scatter according to an integrable factorized $\mathcal{S}$-matrix in $(1+1)$ dimensions.read more
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Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
Enrico Olivucci,Pedro Vieira +1 more
TL;DR: In this article, the authors introduce a notion of ''stampede'' which is a simple time-evolution of a bunch of particles which start their life in a corner and hop their way to the opposite corner through the repeated action of a quantum Hamiltonian.
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Mirror channel eigenvectors of the $d$-dimensional fishnets
TL;DR: In this article, a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in $d$-dimensions is presented.
References
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N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
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Quantum Inverse Scattering Method and Correlation Functions
TL;DR: In this article, a detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well as main models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.
Journal ArticleDOI
Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
TL;DR: The general properties of the factorized S-matrix in two-dimensional space-time are considered in this article, where the relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed.
Journal ArticleDOI
Review of AdS/CFT Integrability: An Overview
Niklas Beisert,Changrim Ahn,Luis F. Alday,Zoltan Bajnok,James M. Drummond,James M. Drummond,Lisa Freyhult,Nikolay Gromov,Nikolay Gromov,Romuald A. Janik,Vladimir Kazakov,Vladimir Kazakov,Thomas Klose,Thomas Klose,Gregory P. Korchemsky,Charlotte Kristjansen,Marc Magro,Marc Magro,Tristan McLoughlin,Joseph A. Minahan,Rafael I. Nepomechie,Adam Rej,Radu Roiban,Sakura Schafer-Nameki,Sakura Schafer-Nameki,Christoph Sieg,Christoph Sieg,Matthias Staudacher,Matthias Staudacher,Alessandro Torrielli,Alessandro Torrielli,Arkady A. Tseytlin,Pedro Vieira,Dmytro Volin,Konstantinos Zoubos +34 more
TL;DR: In this article, the authors present an overview of the achievements and the status of integrability in the context of the AdS/CFT correspondence as of the year 2010.
Book
Form Factors in Completely Integrable Models of Quantum Field Theory
TL;DR: In this paper, the necessary properties of form factors in quantum field theory are discussed, including the necessary conditions of the local commutativity theorem soliton form factor in SG model the properties of operators jm, Tmn, exp(+- i beta u/2) in SU(2)-invariant Thirring model form factor with O(3)-nonlinear s-model asymptotics of form factor current algebras in SU (N) chiral gross-Neveau model.
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