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 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 Z 2 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.

On factorising twists in AdS_3 and AdS_2

“…Drinfeld twists have appeared in recent literature (the most recent to our knowledge being [68]) to 10 Specifically, such statements always refer to the expansion in the variable ξ = e implement deformations, while here we have in a sense undone the twisting to strip the R-matrix down to identity. It would be interesting however to connect the two complementary views.…”

Worldsheet dual of free $\mathcal{N}=2$ quiver gauge theories

“…The theory is therefore best described by reorganising the original N = 4 fields in terms of N = 2 multiplets, and the resulting field content of the N = 2 theory can be represented by a circular quiver, see Figure 1. Quiver theories have been widely studied from an integrability approach [16][17][18][19][20][21][22][23][24][25]. Recently they have also acquired renewed interest thanks to the power of supersymmetric localisation methods [26][27][28][29][30][31][32][33], which lead to some exact results that can be directly compared with supergravity findings [34].…”

Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography

“…In this work we focus on a particular class of theories which are "very close" to the N = 4 SYM theory, namely the N = 2 superconformal quiver theories with gauge group SU(N ) M and bi-fundamental matter. These theories, which can be obtained from D3-branes in Type II B string theory on a Z M orbifold background [23][24][25][26][27], have been extensively studied in integrability contexts [28][29][30][31][32][33][34][35][36][37][38] as well as using localization [39][40][41][42][43][44][45], but mostly at the perturbative level. A related class of models is represented by the N = 2 theories on orientifolds (see for example [27]).…”