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.
Highlights
Distinct realms of theoretical physics find themselves connected through supersymmetric field theories
We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional N = 2 supersymmetric SU(N ) gauge theory with 2N fundamental hypermultiplets
We show that the insertion of a vortex-string type surface defect transverse to the regular monodromy defect on the BPS side amounts to the insertion of the N -dimensional representation of slN on the CFT side
Summary
Distinct realms of theoretical physics find themselves connected through supersymmetric field theories. As the additional evidence for the BPS/CFT correspondence, the fractional quantum T-Q equation is the Fourier transform of the KZ equations for the 4-point conformal block with additional insertion of a degenerate field It is an extension of the statement that the vacuum expectation value of the regular orbifold surface defect in the SU(N ) gauge theory with 2N fundamental hypermultiplets obeys the KZ equation obeyed by the 4-point slN conformal block [43].
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