Phase diagram of 2+1 dimensional field theories and particle-vortex duality

The duality between fundamental particles and solitonic vortex-like
states is one of many remarkable phenomena emerging from quantum field
theories in 2+1 dimensions. This general duality has recently been used
to argue for a larger web of dualities in 2+1 dimensional field
theories. A number of these dualities exchange particle states for
composite objects, and a nontrivial check of such a duality between two
sets of seemingly different degrees of freedom is to study their
thermodynamics as a function of ]both temperature and chemical potential
for particle number. The aim of this project is to understand
particle-vortex duality at finite temperature and in the grand canonical
ensemble, first for Abelian Chern-Simons theories. For non-Abelian
theories some aspects of the thermodynamics have been understood at low
temperatures in the grand canonical ensemble (in the large-N limit).
One goal of this project will be to understand fermion-boson duality in
non-Abelian theories at high temperature and large-N, for generic
values of particle number chemical potential.