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

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.

On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter

“…. , N and α j ∈ (−π, π] [10,62,83]. In the large-N limit, the location of eigenvalues on unit circle can be specified by a continuous distribution function ρ(α) defined by…”

“…presence of chemical potential is obtained by making the substitution α → α − iβµ in the integrand (except in the holonomy distribution ρ(α)) of holonomy integral appearing in the results obtained in this paper at the zero chemical potential. It will be nice to explicitly check if the structure of the results remain the same even in the case when the chemical potential is larger than the thermal mass c B or c F [83]. It seems like, even in the case when |µ| > c B or |µ| > c F , the structure of the results of the correlators of this paper will remain the same; the only modifications will be through the functions χ B (w) and χ F (w) due to the contour deformations of the holonomy integrals away from the unit circle as prescribed in detail in [83].…”

“…Previously there have been numerous computations and checks of this duality in the case of both the massless and massive matter theories at zero temperature. Even the computations have already been performed at finite temperature to compute the thermal free energy of these theories and it has already been shown that the thermal free energies in both the fermionic theories and the bosonic theories map to each other under duality [10,11,62,68,83]. These theories also admit an infinite set of higher spin currents (spin ≥ 1) of single trace operators [1,3,4,14].…”

“…For details about these see e.g. in [3,4,10,11,17,27,62,67,68,83]. 2 In the dimensional regulation scheme, the Chern-Simons levels are renormalized.…”

“…In the large N limit, the renormalized levels and ranks of the two gauge groups are related as κF = −κB and NF = |κB| − NB (see for details e.g. in [17,27,62,67,68,83]). For a precise form of conjectured duality see appendix A of [83].…”