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arXiv · 2608.19619

Moore--Read construction and explicit monodromies of Laughlin states on Riemann surfaces

Kiyoon Eum
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Abstract

We revisit the Moore--Read construction of the $\nu=1/k$ Laughlin states on compact Riemann surfaces, deriving their conformal blocks from $U(1)_k$ Chern--Simons theory through the CS/WZW correspondence. We compute their explicit monodromies under quasi-hole transport and Aharonov--Bohm flux insertion, and conjecture that these coincide with the corresponding adiabatic holonomies. Under this identification, we recover classical results on Laughlin states including the flux-averaged Hall conductance $1/k$ via a vector bundle of Laughlin states over $Jac(\Sigma)$. We also relate our construction to the recently developed algebro-geometric approach to higher genus Laughlin states.

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Kiyoon Eum. 2026-08-20. Moore--Read construction and explicit monodromies of Laughlin states on Riemann surfaces. https://arxiv.org/abs/2608.19619

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