Executive Summary : | The goal of this project is to study collective excitations in interacting topological systems like those that arise in the fractional quantum Hall (FQH) setting. It has been conjectured that in certain FQH states, in particular, the non-Abelian Moore-Read states, there are two collective modes, one of which is fermionic and the other is bosonic. Small system studies have shown that these modes have identical energies in the long-wavelength limit, which is suggestive that there might be an emergent supersymmetry (SUSY) that ensures that these modes have the same mass. The goal of this project is to test this conjecture in detail and find other setting where SUSY could emerge in such strongly interacting topologically ordered systems. |