Evidence for 3d bosonization from monopole operators

Abstract

We give evidence for 3d bosonization in Conformal Field Theories (CFTs) by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level $k$ and $N$ complex bosons in a large $N,k$ expansion. We first consider the $k=0$ case, where we show that scaling dimensions previously computed to subleading order in $1/N$ can be extrapolated to $N=1$ and matched to $O(2)$ Wilson-Fisher CFT scaling dimensions with around 5\% error, which is evidence for particle-vortex duality. We then generalize the subleading calculation to large $N,k$ and fixed $k/N$, extrapolate to $N=k=1$, and consider monopole operators that are conjectured to be dual to non-degenerate scalar operators in a theory of a single Dirac fermion. We find matches typically with 1\% error or less, which is strong evidence of this so-called `seed' duality that implies a web of 3d bosonization dualities among CFTs.

arXiv comment4 pages plus appendices, no figures. v2 minor typos corrected, submitted for publication

References in corpus (38)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Is the Composite Fermion a Dirac Particle?
• Deconfined quantum critical points: symmetries and dualities
• Bootstrapping the O(N) Vector Models
• Seiberg Duality in Chern-Simons Theory
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• 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
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Carving out OPE space and precise $O(2)$ model critical exponents
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Mott Transition in An Anyon Gas
• Monte Carlo study of an improved clock model in three dimensions
• Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
• Conformal dimensions via large charge expansion
• Bosonization and Mirror Symmetry
• A continuous transition between fractional quantum Hall and superfluid states
• On the CFT Operator Spectrum at Large Global Charge
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Monopoles in CP(N-1) model via the state-operator correspondence
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Spontaneously Broken Boosts in CFTs
• The large charge expansion at large N
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Monopole operators from the $4-\epsilon$ expansion
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Large Charge Sector of 3d Parity-Violating CFTs
• Duality and scaling in 3-dimensional scalar electrodynamics
• Monopole scaling dimension using Monte Carlo
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term

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