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 \( {\hat{\mathfrak{sl}}}_N \) 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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ArXiv ePrint: 2103.17186
On leave from: Center for Advanced Studies, Skoltech, and Kharkevich IITP RAS, Moscow, Russia (Nikita Nekrasov).
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Jeong, S., Lee, N. & Nekrasov, N. Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations. J. High Energ. Phys. 2021, 120 (2021). https://doi.org/10.1007/JHEP10(2021)120
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DOI: https://doi.org/10.1007/JHEP10(2021)120