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arXiv · 2103.17186

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

Saebyeok Jeong·Norton Lee·Nikita Nekrasov
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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.

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Saebyeok Jeong, Norton Lee, Nikita Nekrasov. 2021-03-31. Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations. https://doi.org/10.1007/jhep10(2021)120

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