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Q-balls of Quasi-particles in a (2,0)-theory model of the Fractional Quantum Hall Effect (1410.3575v3)

Published 14 Oct 2014 in hep-th

Abstract: A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the $A_1$ (2,0)-theory formulated on $(S1\times R2)/Z_k$, where the generator of $Z_k$ acts as a combination of translation on $S1$ and rotation by $2\pi/k$ on $R2$. At low energy the configuration is described in terms of a 4+1D Super-Yang-Mills theory on a cone ($R2/Z_k$) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged quasi-particles are BPS strings of the (2,0)-theory wrapped on short cycles. We analyze the large $k$ limit, where a smooth cigar-geometry provides an alternative description. In this framework a W-boson can be modeled as a bound state of $k$ quasi-particles. The W-boson becomes a Q-ball, and it can be described as a soliton solution of Bogomolnyi monopole equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from $AdS_3$ to $AdS_2$, and we present some numerical results and an asymptotic expansion.

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