Abstract:
This is the first in a series of papers devoted to the study of spin chains capturing
the spectral problem of 4d N = 2 SCFTs in the planar limit. At one loop and in the
quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the R-matrix
read off from the superpotential. This implies that when orbifolding the N = 4 symmetry
algebra down to the N = 2 one and then marginaly deforming, the broken generators are
not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these
chains are dynamical, in the sense that their Hamiltonian depends on a parameter which
is dynamically determined along the chain. At one loop we map the holomorphic SU(3)
scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose
adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar
SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another
choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These
sectors have a common vacuum state, around which the magnon dispersion relations are
naturally uniformised by elliptic functions. Concretely, for the Z2 quiver theory we study
these dynamical chains by solving the one- and two-magnon problems with the coordinate
Bethe ansatz approach. We confirm our analytic results by numerical comparison with the
explicit diagonalisation of the Hamiltonian for short closed chains.
