3d field theory, plane partitions and triple Macdonald polynomials
- Resource Type
- article
- Authors
- Yegor Zenkevich
- Source
- Journal of High Energy Physics, Vol 2019, Iss 6, Pp 1-25 (2019)
- Subject
- Conformal and W Symmetry
Integrable Field Theories
Matrix Models
Bethe Ansatz
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
- Language
- English
- ISSN
- 1029-8479
Abstract We argue that MacMahon representation of Ding-Iohara-Miki (DIM) algebra spanned by plane partitions is closely related to the Hilbert space of a 3d field theory. Using affine matrix model we propose a generalization of Bethe equations associated to DIM algebra with solutions also labelled by plane partitions. In a certain limit we identify the eigenstates of the Bethe system as new triple Macdonald polynomials depending on an infinite number of families of time variables. We interpret these results as first hints of the existence of an integrable 3d field theory, in which DIM algebra plays the same role as affine algebras in 2d WZNW models.