Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Mykola Dedushenko, Davide Gaiotto

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.

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 super Yang-Mills. The operator algebra in this sector is isomorphic to a truncation of the Yangian . The correlators, encoded in a trace on the Yangian, are controlled by the inhomogeneous spin chain, where 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 super Yang-Mills and integrable spin chains. We also remark on analogous constructions involving half-BPS Wilson lines.

Paper Structure

This paper contains 14 sections, 139 equations, 2 figures.

Table of Contents

  1. Introduction and Conclusions
  2. Outlook
  3. Higgs or D5 presentation
  4. $N$ D3 branes crossing $n$ D5 branes
  5. Fermionic fundamental fields and Wilson lines
  6. $n$ D5 branes between $N$ and $N+n$ D3 branes
  7. $n$ D5 branes between $N$ and $N+n s$ D3 branes
  8. The Coulomb or NS5 perspective
  9. Coproduct.
  10. Traces and transfer matrices
  11. The case of ${\mathcal{A}}_{N;2}$ and ${\mathcal{Y}}[\mathfrak{gl}_2]$
  12. Yangian generators in ${\mathcal{A}}_{N;n}$
  13. Trace and transfer matrices for SQCD
  14. Identity for Q-operators

Figures (2)

  • Figure 1: Local operators live on $S^1\subset S^3$, and $S^3$ is the equator of $S^4$.
  • Figure 2: The balanced quiver that provides the Coulomb branch description of ${\mathcal{A}}^{(s)}_{N;n}$.