A Symmetry Breaking Scenario for QCD${}_3$

Abstract

We consider the dynamics of 2+1 dimensional $SU(N)$ gauge theory with Chern-Simons level $k$ and $N_f$ fundamental fermions. By requiring consistency with previously suggested dualities for $N_f\le 2k$ as well as the dynamics at $k=0$ we propose that the theory with $N_f>2k$ breaks the $U(N_f)$ global symmetry spontaneously to $U(N_f/2+k)\times U(N_f/2-k)$. In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, $2k<N_f<N_{\ast }(N,k)$, with the upper limit $N_{\ast }$ obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at $k=0$. Furthermore, we suggest two scalar dual theories in this range of $N_f$. A similar picture is developed for $SO(N)$ and $Sp(N)$ gauge theories. It sheds new light on monopole condensation and confinement in the $SO(N)$ and $Spin(N)$ theories.

25 pages, 6 figures. v2 added references, minor corrections, new material about symmetry breaking in U(1) gauge theories

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• Generalized Global Symmetries
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• Level/rank Duality and Chern-Simons-Matter Theories
• Seiberg Duality in Chern-Simons Theory
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Bosonization and Mirror Symmetry
• Nonsupersymmetric dualities from mirror symmetry
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
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Cited by in corpus (72)

• On 2-Group Global Symmetries and Their Anomalies
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• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
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• Phases Of Adjoint QCD${}_3$ And Dualities
• Three-dimensional dualities with bosons and fermions
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• Subsystem Non-Invertible Symmetry Operators and Defects
• 3d Abelian Gauge Theories at the Boundary
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
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• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Dualities and Phases of 3D N=1 SQCD
• Anomalies of Generalized Symmetries from Solitonic Defects
• Exceptional Chern-Simons-Matter Dualities
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Living on the walls of super-QCD
• Parity and the modular bootstrap
• From 3d dualities to hadron physics
• Novel 3d bosonic dualities from bosonization and holography
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Metastable Vacua in Large-$N$ QCD${}_3$
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
• Master 3d Bosonization Duality with Boundaries
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
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• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
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• Linking Entanglement and Discrete Anomaly
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
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• Free Energy on the Sphere for Non-Abelian Gauge Theories
• Chern-Simons dualities with multiple flavors at large $N$
• $QC{D}_3$ Dualities and the F-Theorem
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions
• 3D Dualities and Supersymmetry Enhancement from Domain Walls
• The Hilbert Space of large $N$ Chern-Simons matter theories
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Phases of $\mathbf{U}({\mathbf{N}}_{\mathbf{c}})$ QCD${}_3$ from Type 0 Strings and Seiberg Duality
• Fermion-fermion duality in 3+1 dimensions
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Dualities of Adjoint QCD${}_3$ from Branes
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• Phases of Flavor Broken QCD${}_3$
• New and Old Fermionic Dualities from 3d Bosonization
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Cascade of phase transitions in a planar Dirac material
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Dualities of 3D $\mathcal{N}=1$ SQCD from Branes and non-SUSY deformations
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Interface Junctions in QCD${}_4$
• Mildly Flavoring Domain Walls in Sp(N) SQCD
• Boundary gauge and gravitational anomalies from Ward identities
• Time-Reversal Anomalies of QCD${}_3$ and QED${}_3$
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