Abstract
We consider Quantum Electrodynamics in 2 + 1 dimensions with Nf fermionic or bosonic flavors, allowing for interactions that respect the global symmetry U(Nf/2)2. There are four bosonic and four fermionic fixed points, which we analyze using the large Nf expansion. We systematically compute, at order O(1/Nf), the scaling dimensions of quadratic and quartic mesonic operators.We also consider Quantum Electrodynamics with minimal supersymmetry. In this case the large Nf scaling dimensions, extrapolated at Nf = 2, agree quite well with the scaling dimensions of a dual supersymmetric Gross-Neveu-Yukawa model. This provides a quantitative check of the conjectured duality.
Highlights
We find four bosonic and four fermionic fixed points
If the number of flavors Nf is large enough, it is well known that the Renormalization Group (RG) flows in the infrared to a Conformal Field Theory (CFT) describing a second order phase transition
In [1] we showed that the merging pattern of the 4 bosonic and 4 bosonic fixed points suggested by large Nf argument is consistent with various boson ↔ fermion dualities conjectured to hold when the number of flavors is Nf =2 [1, 21, 22]
Summary
We study bosonic QED with large Nf complex scalar fields, imposing at least U(Nf /2) global symmetry. The same graphs can be used to calculate scaling dimension of the bifundamental operators {ΦiΦ ∗j , Φ∗i Φj}, the graph with HS field σ− joining propagators Φ and Φcontributes with the opposite sign compared to the similar graph in the bQED+. In the table 7 we collected all the graphs that contribute to the anomalous scaling dimension of the quartic bifundamental operator |Φk|2+√ |Φk|2 ΦiΦ∗j. Nf we give the list of operators and their scaling dimensions
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