Chern-Simons Theory with Vector Fermion Matter

Abstract

We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R^2 as a function of the 't Hooft coupling lambda=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |lambda|=1; the conformal theory does not exist for |lambda|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W-infinity algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

122 pages, 59 figures. v2: minor corrections, references added

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Symmetries of Holographic Minimal Models
• AdS_4/CFT_3 Construction from Collective Fields
• Correlation Functions in Holographic Minimal Models
• Vector Models in the Singlet Sector at Finite Temperature
• On thermodynamics of N=6 superconformal Chern-Simons theory

Cited by in corpus (304)

• Comments on the Sachdev-Ye-Kitaev model
• QCD and strongly coupled gauge theories: challenges and perspectives
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Convexity and Liberation at Large Spin
• Level/rank Duality and Chern-Simons-Matter Theories
• A Generalization of Sachdev-Ye-Kitaev
• Particle-Vortex Duality from 3d Bosonization
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Black holes in three dimensional higher spin gravity: A review
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• The Higher Spin/Vector Model Duality
• Higher Spins & Strings
• Light-Front Higher-Spin Theories in Flat Space
• One Loop Tests of Higher Spin AdS/CFT
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• An introduction to the SYK model
• Bounding the Space of Holographic CFTs with Chaos
• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• On the uniqueness of higher-spin symmetries in AdS and CFT
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Large N=4 Holography
• Chern Simons duality with a fundamental boson and fermion
• Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory
• The Conformal Bootstrap at Finite Temperature
• Duality between $(2+1)d$ Quantum Critical Points
• Correlators of Large N Fermionic Chern-Simons Vector Models
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• Dual Boundary Conditions in 3d SCFT's
• AdS Description of Induced Higher-Spin Gauge Theory
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Biaxially symmetric solutions to 4D higher-spin gravity
• Bosonization and Mirror Symmetry
• A Symmetry Breaking Scenario for QCD${}_3$
• Nonsupersymmetric dualities from mirror symmetry
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• A universal feature of CFT Renyi entropy
• More Abelian Dualities in 2+1 Dimensions
• Supersymmetric Chern-Simons Theories with Vector Matter
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• Exact results on ABJ theory and the refined topological string
• Solving M-theory with the Conformal Bootstrap
• Duality in N=2 minimal model holography
• Three-dimensional dualities with bosons and fermions
• Direct derivation of "mirror" ABJ partition function
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• Notes on Spinning Operators in Fermionic CFT
• Disorder Operators in Chern-Simons-Fermion Theories
• Constraining conformal field theories with a higher spin symmetry
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• Extended higher spin holography and Grassmannian models
• AdS Maps and Diagrams of Bi-local Holography
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Higher Spin Gravity Amplitudes From Zero-form Charges
• CFT in AdS and boundary RG flows
• The Partition Function of ABJ Theory
• Duality and bosonization of (2+1)d Majorana fermions
• A Derivation of AdS/CFT for Vector Models
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Quantum ${\varphi }^4$ Theory in AdS${}_4$ and its CFT Dual
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• 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 $S^2\times S^1$
• Higher Spin de Sitter Holography from Functional Determinants
• 3d Abelian Gauge Theories at the Boundary
• The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars
• Chern Simons Bosonization along RG Flows
• Veneziano Amplitude of Vasiliev Theory
• Chiral spin liquids on the kagome Lattice
• Vector models and generalized SYK models
• Anomalous Dimensions from Crossing Kernels
• The symmetry of large N=4 holography
• Double copy structure of parity-violating CFT correlators
• From Higher Spins to Strings: A Primer
• Non-Abelian 3d Bosonization and Quantum Hall States
• Partition Functions for Higher-Spin theories in AdS
• Comments on higher-spin holography
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• One-loop Finiteness of Chiral Higher Spin Gravity
• Spontaneous Breaking of Scale Invariance in a d=3 U(N) Model with Chern-Simons Gauge Field
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• Embedding three-dimensional bosonization dualities into string theory
• Chern-Simons Matter Theories and Higher Spin Gravity
• Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
• Homotopy Operators and Locality Theorems in Higher-Spin Equations
• QCD domain walls, Chern-Simons theories and holography
• Momentum space parity-odd CFT 3-point functions
• Chern-Simons-Fermion Vector Model with Chemical Potential
• Light States in Chern-Simons Theory Coupled to Fundamental Matter
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Supersymmetric Higher Spin Theories
• Superspace formulation and correlation functions of 3d superconformal field theories
• A master bosonization duality
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• The Exact Renormalization Group and Higher-spin Holography
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Fermions in AdS and Gross-Neveu BCFT
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Transport in Chern-Simons-Matter Theories
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Multiparticle extension of the higher-spin algebra
• Correlators in W_N Minimal Model Revisited
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Perturbations of W(infinity) CFTs
• Bosonizing three-dimensional quiver gauge theories
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Large N Renormalization Group Flows in 3d $\mathcal{N}=1$ Chern-Simons-Matter Theories
• Dualities and Phases of 3D N=1 SQCD
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• Formal Higher Spin Gravities
• On the Local Frame in Nonlinear Higher-Spin Equations
• 3d Abelian Dualities with Boundaries
• One-loop Test of Free SU(N) Adjoint Model Holography
• A Crack in the Conformal Window
• Exceptional Chern-Simons-Matter Dualities
• Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• Smoothed Transitions in Higher Spin AdS Gravity
• Higher Spin ANEC and the Space of CFTs
• A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Test of the local form of higher-spin equations via AdS/CFT
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Extended supersymmetry in AdS_3 higher spin theories
• On holomorphic sector of higher-spin theory
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• More on Chiral Higher Spin Gravity and Convex Geometry
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• On current contribution to Fronsdal equations
• 3D Field Theories with Chern--Simons Term for Large $N$ in the Weyl Gauge
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Four-point functions in large $N$ Chern-Simons fermionic theories
• Higher-spin currents in the Gross-Neveu model at $1/n^2$
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Novel 3d bosonic dualities from bosonization and holography
• On the Holography of Free Yang-Mills
• Higher spin currents in the critical $O(N)$ vector model at $1/N^2$
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Phases of QCD${}_3$ from Non-SUSY Seiberg Duality and Brane Dynamics
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory
• Vector model in various dimensions
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Metastable Vacua in Large-$N$ QCD${}_3$
• The $L_{\infty }$ structure of gauge theories with matter
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Quantizing Carrollian field theories
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Chern-Simons-Ghost Theories and de Sitter Space
• Large N Chern-Simons with massive fundamental fermions - A model with no bound states
• One-loop effective actions and higher spins
• Perturbative and Non-Perturbative Aspects in Vector Model/Higher Spin Duality
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Dualities from higher-spin supergravity
• Chiral Higher Spin Gravity and Convex Geometry
• Dense Chern-Simons Matter with Fermions at Large N
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• $3d$ fermion-boson map with imaginary chemical potential
• Mirror Symmetry and Bosonization in 2d and 3d
• The Massive Fermion Phase for the U(N) Chern-Simons Gauge Theory in D=3 at Large N
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• A semi-local holographic minimal model
• Three-dimensional fractional-spin gravity
• Chern-Simons theory coupled to bifundamental scalars
• A Stringy theory in three dimensions and Massive Higher Spins
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Black holes from large N singlet models
• Large Charge Sector of 3d Parity-Violating CFTs
• Double-Trace Flows and the Swampland
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Quartic locality of higher-spin gravity in de Sitter and Euclidean anti-de Sitter space
• Supersymmetry Breaking and the Cosmological Constant
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• ABJ Quadrality
• The fermion-boson map for large d
• The a-function in three dimensions: beyond leading order
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Higher Spin Gravities and Presymplectic AKSZ Models
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• One-loop effective actions and higher spins. II
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• On Superconformal Anyons
• Planar solutions of higher-spin theory I: free field level
• Vacuum structure of large $N$ QCD${}_3$ from holography
• Matter Chern Simons Theories in a Background Magnetic Field
• 3d N=4 Bootstrap and Mirror Symmetry
• Anyonic correlation functions in Chern-Simons matter theories
• Low Tension Strings on a Cosmological Singularity
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• On (Un)Broken Higher-Spin Symmetry in Vector Models
• Chern-Simons Theory on Seifert Manifold and Matrix Model
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Dualities and bosonization of massless fermions in three dimensional space-time
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Conformal Truncation of Chern-Simons Theory at Large $N_f$
• Charting the phase diagram of QCD${}_3$
• Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model
• Machine Learning Etudes in Conformal Field Theories
• Mass-deformed $\mathcal{N}=3$ Supersymmetric Chern-Simons-Matter Theory
• Higher Spin Fronsdal Equations from the Exact Renormalization Group
• Anyon Scattering from Lightcone Hamiltonian: the Singlet Channel
• Anomalous dimensions of higher spin currents in large N CFTs
• Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• Breaking conformal invariance- Large N Chern-Simons theory coupled to massive fundamental fermions
• Non-Abelian Fermionization and Fractional Quantum Hall Transitions
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• Chern-Simons dualities with multiple flavors at large $N$
• A CFT Distance Conjecture
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Evidence for 3d bosonization from monopole operators
• Even spin $\mathcal{N}=4$ holography
• $QC{D}_3$ Dualities and the F-Theorem
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• From Phase Space to Integrable Representations and Level-Rank Duality
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry
• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Three-dimensional Yang-Mills Chern-Simons theory from D3-brane background with D-instantons
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Pre-ADS Superpotential from Confined Monopoles
• Constructing the bulk at the critical point of three-dimensional large $N$ vector theories
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• ABJ Theory in the Higher Spin Limit
• One-dimensional bosonization and the SYK model
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Spectral sum rules for conformal field theories in arbitrary dimensions
• The masses of higher spin fields on AdS_4 and conformal perturbation theory
• Infinite distances in multicritical CFTs and higher-spin holography
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Fermion-fermion duality in 3+1 dimensions
• The Conformal Spectrum of Non-Abelian Anyons
• 3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality
• Topological string entanglement
• Phases of $\mathbf{U}({\mathbf{N}}_{\mathbf{c}})$ QCD${}_3$ from Type 0 Strings and Seiberg Duality
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Holographic ${\mathrm{QCD}}_3$ and Chern-Simons theory from anisotropic supergravity
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• New Phase Transitions in Chern-Simons Matter Theory
• The Analytic Bootstrap for Large $N$ Chern-Simons Vector Models
• Holographic Chern-Simons Defects
• AdS from CFT for scalar QED
• QED's in $2+1$ dimensions: complex fixed points and dualities
• Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT
• Instantons in AdS${}_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT${}_3$'s
• Non-Minimal Higher-Spin DS4/CFT3
• Scalar Correlators in Bosonic Chern-Simons Vector Models
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories
• 4D Flat-space scattering amplitude /$CF{T}_3$ correlator correspondence revisited
• Phases of Flavor Broken QCD${}_3$
• Chern-Simons-Matter Theories at Large Baryon Number
• Indirect detection of Cosmological Constant from interacting open quantum system
• Massive fermion model in 3d and higher spin currents
• Roton-phonon excitations in Chern-Simons matter theory at finite density
• Stringy Symmetries and the Higher Spin Square
• Scaling and Diffusion of Dirac Composite Fermions
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities
• On correlation functions as higher-spin invariants
• Conformal correlators in the critical $O(N)$ vector model
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Emergent Supersymmetry at Large $N$
• Tensor Field Theories: Renormalization and Random Geometry
• Holographic de Sitter Spacetime and Quantum Corrections to The Cosmological Constant
• Large N Thirring Matter in Three Dimensions
• Flavor Broken QCD${}_3$ at Large N
• Higher Spin Gravity and Exact Holography
• DNA Mutations via Chern-Simons Currents
• Higher spin holography with Galilean symmetry in general dimensions
• 3d Large $N$ Vector Models at the Boundary
• Dualities in 3D Large $N$ Vector Models
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Large N limit of supersymmetric Chern-Simons-matter model: breakdown of superconformal symmetry
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter
• Renormalized Schwinger-Dyson functional
• Superconformal field theory in three dimensions: Correlation functions of conserved currents
• Bootstrap and collider physics of parity violating conformal field theories in $d=3$
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$
• SUSY Breaking in Monopole Quivers
• Confinement and Flux Attachment