Q-balls of quasi-particles in a (2,0)-theory model of the fractional quantum Hall effect

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 (S-1 x R-2)/Z(k), where the generator of Z(k) acts as a combination of translation on S-1 and rotation by 2 pi/k on R-2. At low energy the configuration is described in terms of a 4+1D Supe-rYang-Mills theory on a cone (R-2/Z(k)) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged "quasiparticles" 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.