Geometry and large N limits in Laughlin states
arXiv:1608.02928
Abstract
In these notes I survey geometric aspects of the lowest Landau level wave functions, integer quantum Hall state and Laughlin states on compact Riemann surfaces. In particular, I review geometric adiabatic transport on the moduli spaces, derivation of the electromagnetic and gravitational anomalies, Chern-Simons theory and adiabatic phase, and the relation to holomorphic line bundles, Quillen metric, regularized spectral determinants, bosonisation formulas on Riemann surfaces and asymptotic expansion of the Bergman kernel.
arXiv comment65 pages, 4 figures, Lecture notes from the School on Geometry and Quantization, ICMAT, Madrid, September 7-11, 2015, v2: glitch in Fig. 4 fixed, minor changes
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