QED's in $2+1$ dimensions: complex fixed points and dualities

Abstract

We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2{)}^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2{)}^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFT's. In the bosonic QED's the merging happens around $N_f\sim 9-11$ and does not break the global symmetry. In the fermionic QED's the merging happens around $N_f\sim 3-7$ and breaks $U(N_f)$ to $U(N_f/2{)}^2$. When $N_f=2$, we show that all four bosonic fixed points are one-to-one dual to the fermionic fixed points. The merging pattern suggested at large $N_f$ is consistent with the four $N_f=2$ boson $\lra$ fermion dualities, providing support to the validity of the scenario.

arXiv comment22 pages, many figures

References in corpus (33)

• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Deconfined quantum critical points: symmetries and dualities
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Duality between $(2+1)d$ Quantum Critical Points
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Scale-invariance of parity-invariant three-dimensional QED
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• Quantum Electrodynamics in d=3 from the epsilon-expansion
• Three-dimensional dualities with bosons and fermions
• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• Duality and bosonization of (2+1)d Majorana fermions
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• On the Possibility of Second-Order Phase Transitions in Spontaneously Broken Gauge Theories
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Addendum to "Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge"
• Critical number of fermions in three-dimensional QED

Cited by in corpus (4)

• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions
• Charged and neutral fixed points in the O(N)+O(N)-model with Abelian gauge fields