  We propose an interesting BPS/CFT correspondence playground: the correlation
function of two intersecting half-BPS surface defects in four-dimensional
$\mathcal{N}=2$ 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 $\widehat{\mathfrak{sl}}_N$ current algebra with one of the vertex
operators corresponding to the $N$-dimensional $\mathfrak{sl}_N$
representation, which we demonstrate with the help of the
Knizhnik-Zamolodchikov equation. We also identify the correlator with a state
of the $XXX_{\mathfrak{sl}_2}$ spin chain of $N$ Heisenberg-Weyl modules over
$Y(\mathfrak{sl}_2)$. We discuss the associated quantum Lax operators, and
connections to isomonodromic deformations.
