Surface defects and elliptic quantum groups

Abstract

A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional $\mathcal{N}=1$ supersymmetric field theories as transfer matrices related to elliptic quantum groups.

31 pages. v2: minor changes and corrections; v3: minor improvements, published version

References in corpus (6)

• Dimer models and toric diagrams
• Supersymmetric gauge theory and the Yangian
• Quivers, YBE and 3-manifolds
• Branes and integrable lattice models
• Continuous biorthogonality of the elliptic hypergeometric function
• The elliptic GL(n) dynamical quantum group as an h-Hopf algebroid

Cited by in corpus (23)

• 5d Partition Functions with A Twist
• A slow review of the AGT correspondence
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Flavored surface defects in 4d N=1 SCFTs
• Superspin chains from superstring theory
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Surface defects in E-string compactifications and the van Diejen model
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Defect multiplets of N=1 supersymmetry in 4d
• 't Hooft lines of ADE-type and Topological Quivers
• Integrable lattice spin models from supersymmetric dualities
• Wilson-'t Hooft lines as transfer matrices
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• A freely generated ring for N=1 models in class S_k
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• Integrable 3D lattice model in M-theory
• An infrared bootstrap of the Schur index with surface defects
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Integrability As Duality: The Gauge/YBE Correspondence