Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

Saebyeok Jeong, Norton Lee, Nikita Nekrasov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional N = 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the sl̂ N current algebra with one of the vertex operators corresponding to the N-dimensional slN representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the XXXsl2 spin chain of N Heisenberg-Weyl modules over Y (sl2). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

Original languageEnglish
Article number120
JournalJournal of High Energy Physics
Issue number10
Publication statusPublished - Oct 2021
Externally publishedYes


  • Integrable Hierarchies
  • Nonperturbative Effects
  • Supersymmetric Gauge Theory
  • Supersymmetry and Duality


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