  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.
