Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type (2503.15446v1)

Published 19 Mar 2025 in hep-th, math-ph, math.AG, math.MP, and math.RT

Abstract: We study BPS loop operators in a 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the anti-symmetric representation. The algebra of BPS loop operators in the $\Omega$-background provides a deformation quantization of the Coulomb branch, which is expected to coincide with the quantized K-theoretic Coulomb branch in the mathematical literature. For the rank-one case, i.e., $Sp(1) \simeq SU(2)$, we show that the quantization of the Coulomb branch, evaluated using the supersymmetric localization formula, agrees with the polynomial representation of the spherical part of the double affine Hecke algebra (spherical DAHA) of $(C_1{\vee}, C_1)$-type. For higher-rank cases, where $N \geq 2$, we conjecture that the quantized Coulomb branch of the 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory is isomorphic to the spherical DAHA of $(C_N{\vee}, C_N)$-type . As evidence for this conjecture, we demonstrate that the quantization of an 't Hooft loop agrees with the Koornwinder operator in the polynomial representation of the spherical DAHA.

Summary

We haven't generated a summary for this paper yet.