Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
Exact Results for 't Hooft Loops in Gauge Theories on S^4
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abstract
The path integral of a general N=2 supersymmetric gauge theory on S^4 is exactly evaluated in the presence of a supersymmetric 't Hooft loop operator. The result we find - obtained using localization techniques - captures all perturbative quantum corrections as well as non-perturbative effects due to instantons and monopoles, which are supported at the north pole, south pole and equator of S^4. As a by-product, our gauge theory calculations successfully confirm the predictions made for 't Hooft loops obtained from the calculation of topological defect correlators in Liouville/Toda conformal field theory.
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Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type
Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.