Abstract
We study the fate of weakly coupled dual QED3 in the infrared, that is, a single two-component Dirac fermion coupled to an emergent U(1) gauge field, but without Chern-Simons term. This theory has recently been proposed as a dual description of 2D surfaces of certain topological insulators. Using the renormalization group, we find that the interplay of gauge fluctuations with generated interactions in the four-fermi sector stabilizes an interacting conformal field theory (CFT) with finite four-fermi coupling in the infrared. The emergence of this CFT is due to cancellations in the $\beta$-function of the four-fermi coupling special to "NF = 1/2". We also quantify how a possible "strong" Dirac fermion duality between a free Dirac cone and dual QED3 would constrain the universal constants of the topological current correlator of the latter.
Highlights
Be generated under a renormalization group (RG) flow, such as four-fermi interactions and radiative corrections to the propagators
We study the fate of weakly coupled dual QED3 in the infrared, that is, a single two-component Dirac fermion coupled to an emergent U(1) gauge field, but without Chern-Simons term
We find that the interplay of gauge fluctuations with generated interactions in the four-fermi sector stabilizes an interacting conformal field theory (CFT) with finite four-fermi coupling in the infrared
Summary
Our main result is that eq (1.1), if initially weak-to-moderately coupled, flows toward an interacting conformal field theory (CFT) in the infrared in which generated four-fermi couplings attain finite values. In the condensed matter context of dual QED3 as a surface description for topological insulators, this implies that interactions preserve the gapless responses and the system remains a topological (semi-)metal at lowest energies This result is derived and presented in subsection 4.1. We find that gauge fluctuations never destabilize the four-fermi sector toward symmetry-breaking sufficiently strongly; instead, the flow is always attracted toward an infrared stable fixed-point for the four-fermi coupling, which preserves the scaling/conformal symmetry of the gauge sector. The main scope of this work was an investigation of the symmetry breaking patterns of QED3, including chiral channels, by detection of runaway flows for fermionic couplings caused by fixed point annihilation. To set the stage for dual QED3, we recapitulate the key elements of this analysis
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