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Title:
Geometry and Large N limits in Laughlin states
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Abstract:
We consider integer QHE states and Laughlin states on Riemann surfaces with arbitrary metric and complex structure. We derive generating functional for the density of states and compute transport coefficients for the adiabatic transport on the moduli space, in the limit of large number of particles. In addition to Hall conductance and anomalous Hall viscosity, a novel coefficient transpires on moduli spaces of surfaces of genus 2 and higher, due to the gravitational anomaly. We also show that the adiabatic phase acquired by the (integer QHE) wave function under the adiabatic transport, is given by the gauge and gravitational Chern-Simons functional. Finally, we discuss recent results for singular (conical) Riemann surfaces, where the gravitational anomaly effects transpire most prominently.
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