FRACTIONAL QUANTUM HALL EFFECTS AT SMALL FILLING FRACTION, QUASIPARTICLES, AND THE (2,0)-THEORY
Nesty Torres-Chicon, Ori Ganor.
University of California, Berkeley, Berkeley, CA.
The fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A1 (2,0)-theory formulated on (S1 x R2)/Zk, where the generator of Zk acts as a combination of translation on S1 and rotation by 2Ï€/k on R2. At low-energy, the theory is described in terms of a 4+1D super-Yang-Mills theory on a cone (R2/Zk) with additional 2+1D degrees of freedom at the tip of the cone. Fractionally charged quasi-particles have a natural description in terms of BPS strings of the (2,0) theory. We analyze the large k limit where a smooth cigar geometry provides an alternative description. In this framework, a W-boson can be viewed as a bound state of k quasi-particles. The W-boson is described by a soliton solution of BPS equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from AdS3 to AdS2, and we present some numerical solutions.