Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Abstract

This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 symmetry algebra down to the $$ \mathcal{N} $$ 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.

4D $\boldsymbol{\mathcal{N}}\mathbf{=}$ 2 SCFTs and spin chains

“…In what comes we will concentrate to the φ-vacua. A study of the Q-vacuum is not yet available in the literature, but it reveals very interesting properties and is work in progress [54].…”

“…for the trigonometric and elliptic models, respectively. We believe that it should be possible to take this path via combining the insights from the works of [54,65,67,68,83].…”

String junctions suspended between giants

“…it is expected that N = 2 structure at higher loop orders might help to elucidate how this works in detail. We would like to highlight that there is a program where some of these computation have been done in in the closed spin chain setup [33,[37][38][39].…”

Giant Gravitons Intersecting at Angles from Integrable Spin Chains

“…If the so-called "string hypothesis" is true in some form, then one can expect that all integrable open chains have such a description. Cases of particular interest also include the non-integrable spin chains arising from more realistic gauge theories such as large N QCD [28], Lagrangian superconformal theories with less supersymmetry [29], or fishnet theories [30]. Our methods provide a starting point to probe the bulk string dual of other large N gauge theories.…”