Abstract
In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as mathfrak{gl} (1) affine Yangian “spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with the affine Yangian R-matrix and derive Bethe ansatz equations for the spectrum. Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.
Highlights
Structures, such as Fateev models or quantum AKNS model
Alexey Litvinova,b and Ilya Vilkoviskiyb,c aLandau Institute for Theoretical Physics, Akademika Semenova av. 1A, Chernogolovka 142432, Russia bCenter for Advanced Studies, Skolkovo Institute of Science and Technology, 1 Nobel Street, Moscow 143026, Russia cFaculty of Mathematics, National Research University Higher School of Economics, Usacheva 6, Moscow 119048, Russia E-mail: litvinov@itp.ac.ru, reminguk@gmail.com. In these notes we study integrable structures of conformal field theory with BCD symmetry
Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras
Summary
The theories (2.3) are known to be integrable both classically and quantum mechanically They share an interesting property of the duality Sometimes it may be convenient to use the notation Ri,j(ui − uj) in order to emphasise the value of the zero mode (see (3.3)) This reflection operator can be defined up to a normalisation factor from the condition (Q = √1+ 2 ). In order to introduce the K-operator, we consider rank two W algebras of BCD type They can be defined as commutants of screening operators (here b = √ 2 ). It is interesting to note that K1, K2 and K3 seem to exhaust all solutions to KRKR equation (3.12) which preserve the grading operator W2dz This is an unproven statement, confirmed by explicit calculations on lower levels
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