TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.8.1.003
TI  - R-matrices and Miura operators in 5d Chern-Simons theory
PY  - 2025/01/13
UR  - https://scipost.org/SciPostPhysCore.8.1.003
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 8
IS  - 1
SP  - 003
A1  - Ishtiaque, Nafiz
AU  - Jeong, Saebyeok
AU  - Zhou, Yehao
AB  - We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$ Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of $\mathfrak{gl}(1)$, satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products.
ER  -

@Article{10.21468/SciPostPhysCore.8.1.003,
	title={{R-matrices and Miura operators in 5d Chern-Simons theory}},
	author={Nafiz Ishtiaque and Saebyeok Jeong and Yehao Zhou},
	journal={SciPost Phys. Core},
	volume={8},
	pages={003},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.8.1.003},
	url={https://scipost.org/10.21468/SciPostPhysCore.8.1.003},
}