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

TL;DR

This paper models fractional quantum Hall effect phenomena using a (2,0)-theory framework, revealing that W-bosons can be viewed as Q-balls formed from bound states of fractionally charged quasi-particles, with insights from monopole equations and curved space solutions.

Contribution

It introduces a novel (2,0)-theory based toy model for fractional quantum Hall effect, connecting quasi-particles to BPS strings and soliton solutions in a curved space setting.

Findings

W-bosons modeled as bound states of quasi-particles

Q-balls described as solitons of monopole equations

Numerical and asymptotic analysis of solutions

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 $(S^1\times R^2)/Z_k$, 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 Super-Yang-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 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.