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

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arxiv 2103.17186 v4 pith:QYGXW4S2 submitted 2021-03-31 hep-th math-phmath.AGmath.MPmath.QAmath.RT

Saebyeok Jeong , Norton Lee , Nikita Nekrasov This is my paper · ORCID
classification hep-thmath-phmath.AGmath.MPmath.QAmath.RT
keywords mathfrakquantumdefectsequationgaugeintersectingknizhnik-zamolodchikovoperators
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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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Cited by 5 Pith papers

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