Matter Chern Simons Theories in a Background Magnetic Field

Abstract

We study large $N$ 2+1 dimensional fermions in the fundamental representation of an $SU(N{)}_k$ Chern Simons gauge group in the presence of a uniform background magnetic field for the $U(1)$ global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t' Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t'Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large $N$ fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.

arXiv comment95 pages, 11 figures

References in corpus (48)

• String Theory and Noncommutative Geometry
• Noncommutative Perturbative Dynamics
• AdS Dual of the Critical O(N) Vector Model
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Massless Higher Spins and Holography
• Noncommutative Solitons
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Level/rank Duality and Chern-Simons-Matter Theories
• The complete superconformal index for N=6 Chern-Simons theory
• Index for three dimensional superconformal field theories with general R-charge assignments
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Particle-Vortex Duality from 3d Bosonization
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Nonperturbative aspects of ABJM theory
• Non-factorizable Contributions to $B\to \pi \pi$ Decays
• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Chern Simons duality with a fundamental boson and fermion
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Correlators of Large N Fermionic Chern-Simons Vector Models
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• Particle-vortex duality in topological insulators and superconductors
• Phases Of Adjoint QCD${}_3$ And Dualities
• On Noncommutative Solitons
• Supersymmetric Chern-Simons Theories with Vector Matter
• Unstable Solitons in Noncommutative Gauge Theory
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• Disorder Operators in Chern-Simons-Fermion Theories
• Duality and bosonization of (2+1)d Majorana fermions
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Unitarity, Crossing Symmetry and Duality in the scattering of $\mathcal{N}=1$ Susy Matter Chern-Simons theories
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Chern Simons Bosonization along RG Flows
• Veneziano Amplitude of Vasiliev Theory
• Chern-Simons-Fermion Vector Model with Chemical Potential
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$

Cited by in corpus (12)

• Constraining momentum space correlators using slightly broken higher spin symmetry
• The $L_{\infty }$ structure of gauge theories with matter
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Anyonic correlation functions in Chern-Simons matter theories
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Chern-Simons-Matter Theories at Large Baryon Number