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

A bstract We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $$ \mathcal{N} N = 2 supersymmetric SU( N ) gauge theory with fundamental hypermultiplets. show it satisfies a difference equation, fractional quantum T-Q relation . Its Fourier transform is 5-point conformal block {\hat{\mathfrak{sl}}}_N sl ̂ current algebra one vertex operators corresponding to -dimensional {\mathfrak{sl}}_N representation, which we demonstrate help Knizhnik-Zamolodchikov equation. also identify correlator state {XXX}_{{\mathfrak{sl}}_2} XXX 2 spin chain Heisenberg-Weyl modules over Y ( {\mathfrak{sl}}_2 ). discuss associated Lax operators, and connections isomonodromic deformations.