A 6D topological field theory of abelian three-form potentials

6D Fractional Quantum Hall Effect

We present a 6d generalization of the fractional quantum hall effect in the presence of a large background four-form flux.The low energy physics is governed by a bulk7d topological field theory of abelian three-form potentials with a single derivative chern-simons-like action coupled to a 6d anti-chiral theory of effective strings.We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6d superconformal field theories correspond to a hierarchy of excited states.Using methods from conformal field theory we also compute the analog of the laughlin wavefunction.We also show that a supersymmetric version of the 7d theory embeds in m-theory, and can be decoupled from gravity.