Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle

TL;DR

This paper extends the understanding of Chern-Simons matter theories by deriving a generalized occupation number formula that reveals a bosonic exclusion principle, leading to a stable Bose condensate phase at high chemical potential.

Contribution

It provides an explicit finite 't Hooft coupling formula for quasiparticle occupation numbers, revealing a new bosonic exclusion principle and phase diagram structure in Chern-Simons theories.

Findings

Derived a generalized Bose-Einstein occupation number formula for Chern-Simons bosons.

Discovered a bosonic exclusion principle limiting boson occupation per state.

Identified a stable Bose condensed phase at high chemical potential.

Abstract

We generalize previously obtained results for the (all orders in the 't Hooft coupling) thermal free energy of bosonic and fermionic large $N$ Chern-Simons theories with fundamental matter, to values of the chemical potential larger than quasiparticle thermal masses. Building on an analysis by Geracie, Goykhman and Son, we present a simple explicit formula for the occupation number for a quasiparticle state of any given energy and charge as a function of the temperature and chemical potential. This formula is a generalization to finite 't Hooft coupling of the famous occupation number formula of Bose-Einstein statistics, and implies an exclusion principle for Chern-Simons coupled bosons: the total number of bosons occupying any particular state cannot exceed the Chern-Simons level. Specializing our results to zero temperature we construct the phase diagrams of these theories as a function of chemical potential and the UV parameters. At large enough chemical potential, all the bosonic theories we study transit into a compressible Bose condensed phase in which the runaway instability of free Bose condensates is stabilized by the bosonic exclusion principle. This novel Bose condensate is dual to - and reproduces the thermodynamics of - the fermionic Fermi sea.