Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain

Abstract

We study algebras and correlation functions of local operators at half-BPS interfaces engineered by the stacks of D5 or NS5 branes in the 4d $\mathcal{N}=4$ super Yang-Mills. The operator algebra in this sector is isomorphic to a truncation of the Yangian $\mathcal{Y}({\mathfrak{gl}}_n)$. The correlators, encoded in a trace on the Yangian, are controlled by the inhomogeneous ${\mathfrak{sl}}_n$ spin chain, where $n$ is the number of fivebranes: they are given in terms of matrix elements of transfer matrices associated to Verma modules, or equivalently of products of Baxter's Q-operators. This can be viewed as a novel connection between the $\mathcal{N}=4$ super Yang-Mills and integrable spin chains. We also remark on analogous constructions involving half-BPS Wilson lines.

48 pages, 7 figures; v2: references added

References in corpus (8)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Wilson Loops of Anti-symmetric Representation and D5-branes
• A Shortcut to the Q-Operator
• Baxter Q-Operators and Representations of Yangians
• Bethe/Gauge correspondence on curved spaces
• Sphere correlation functions and Verma modules
• Quantum Spin Systems and Supersymmetric Gauge Theories, I

Cited by in corpus (3)

• Lax Operator and superspin chains from 4D CS gauge theory
• Integrable 3D lattice model in M-theory
• One-point functions for doubly-holographic BCFTs and backreacting defects