Dense Chern-Simons matter with fermions at large N

Abstract

In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the 't Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

Matter Chern Simons theories in a background magnetic field

“…As the RHS of (4.128) is a continuous function of ζ ex , it follows that it takes every real value as ζ ex varies from −∞ to ∞, except possibly the extreme value λ F = ±1. 35 As a consequence (4.128) has at least one real solution (for the variable ζ ex ) for every choice of m F provided |λ F | < 1. It is easily verified that this conclusion continues to hold for negative bands and also for exceptional bands.…”

“…Second because these theories are solvable in the large N limit [4]. Third because the all orders large N solution of various quantities (like S matrices [20][21][22][23][24][25] and thermal partition functions [4,[26][27][28][29][30][31][32][33][34][35][36][37][38][39]), apart from supplying overwhelming evidence for duality, reveal qualitatively novel dynamics. 2 Fourth because these theories have interesting conjectured bulk dual descriptions in terms of Vasiliev theory.…”

Abelian Chern-Simons vortices at finite chemical potential

“…Eventually, we would like to understand finite density vortex solutions in SU (N ) and U (N ) Chern-Simons-scalar theories where finite chemical potential results in condensation of gauge fields, potentially breaking rotational invariance [9] 1 . A broader aim for exploring different aspects of finite density physics in Chern-Simonsmatter theories is to understand the implications of the associated web [12][13][14] of particle-vortex and Bose-Fermi dualities in 2+1 dimensions [15][16][17][18][19][20][21][22][23].…”

Chern-Simons dualities with multiple flavors at large N

“…One important exception is that of Chern-Simons matter theories in an 't Hooft limit. These theories give us a theoretical lamppost, under which we can reliably compute many observables, like the S-matrix of massive phases [1][2][3], operator product expansion (OPE) coefficients at fixed points [4][5][6][7], finite temperature response functions [8][9][10][11], and so on.…”