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# High Energy Physics - Theory

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

(Submitted on 31 Mar 2021 (v1), last revised 27 Oct 2021 (this version, v3))

Abstract: 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.

## Submission history

From: Saebyeok Jeong [view email]**[v1]**Wed, 31 Mar 2021 16:15:34 GMT (1523kb,D)

**[v2]**Sat, 16 Oct 2021 21:42:22 GMT (1525kb,D)

**[v3]**Wed, 27 Oct 2021 16:24:19 GMT (1525kb,D)

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