AI 中文总结
该研究重新探讨黎曼面上ν=1/k Laughlin态的Moore–Read构造，通过CS/WZW对应推导共形块，计算其单值群并关联绝热环绕子，得到经典结果并联系高亏格态的代数几何方法。
AI 中文摘要
我们重新研究紧致黎曼面上ν=1/k的Laughlin态的Moore–Read构造，通过CS/WZW对应从U(1)_k Chern–Simons理论推导其共形块。我们计算了准空穴输运和Aharonov–Bohm磁通插入下的显式单值群，并猜想其与相应绝热环绕子一致。在此对应下，我们通过Jac(Σ)上的Laughlin态向量丛，得到了关于Laughlin态的经典结果，包括磁通平均霍尔电导1/k。我们还将我们的构造与近期发展的高亏格Laughlin态的代数几何方法联系起来。
英文摘要
We revisit the Moore--Read construction of the $ν=1/k$ 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 $Jac(Σ)$. We also relate our construction to the recently developed algebro-geometric approach to higher genus Laughlin states.
Comments24 pages
