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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Quantized Coulomb branch of 4d 𝒩 = 2 Sp(N) gauge theory and spherical DAHA of (CN∨ ,CN)-type

  • Yutaka Yoshida1
  1. 1Meiji Gakuin University
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Abstract

We study BPS loop operators in a 4d 𝒩 = 2 Sp(N) gauge theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the antisymmetric representation. The algebra of BPS loop operators in the Ω-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) ≃ 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 (C1∨ ,C1)-type. For higher-rank cases, where N ≥ 2, we conjecture that the quantized Coulomb branch of the 4d 𝒩 = 2 Sp(N) gauge theory is isomorphic to the spherical DAHA of (CN∨ ,CN)-type. As evidence for this conjecture, we show that the quantization of an ’t Hooft loop agrees with the Koornwinder operator in the polynomial representation of the spherical DAHA.

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Cite

BibTeXRIS
BibTeX
@article{yoshida2026quantized,
  title = {{Quantized Coulomb branch of 4d 𝒩 = 2 Sp(N) gauge theory and spherical DAHA of $$ \left(C_N^\vee ,C_N\right) $$-type}},
  author = {Yutaka Yoshida},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)031},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)031},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Quantized Coulomb branch of 4d 𝒩 = 2 Sp(N) gauge theory and spherical DAHA of (C_N^∨ ,C_N)-type
AU  - Yutaka Yoshida
PY  - 2026
DA  - 2026/11/04
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)031
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)031
AB  - We study BPS loop operators in a 4d 𝒩 = 2 Sp(N) gauge theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the antisymmetric representation. The algebra of BPS loop operators in the Ω-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) ≃ 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^∨ ,C_1)-type. For higher-rank cases, where N ≥ 2, we conjecture that the quantized Coulomb branch of the 4d 𝒩 = 2 Sp(N) gauge theory is isomorphic to the spherical DAHA of (C_N^∨ ,C_N)-type. As evidence for this conjecture, we show that the quantization of an ’t Hooft loop agrees with the Koornwinder operator in the polynomial representation of the spherical DAHA.
SN  - 1029-8479
ER  -