Quantum Electrodynamics ind=3from theεExpansion

Abstract

We study Quantum Electrodynamics in d = 3 (QED3) coupled to N f flavors of fermions. The theory flows to an IR fixed point for N f larger than some critical number N c f . For N f ≤ N c f , chiralsymmetry breaking is believed to take place. In analogy with the Wilson-Fisher description of the critical O(N ) models in d = 3, we make use of the existence of a fixed point in d = 4 − 2 to study the three-dimensional conformal theory. We compute in perturbation theory the IR dimensions of fermion bilinear and quadrilinear operators. For small N f , a quadrilinear operator can become relevant in the IR and destabilize the fixed point. Therefore, the -expansion can be used to estimate N c f . An interesting novelty compared to the O(N ) models is that the theory in d = 3 has an enhanced symmetry due to the structure of 3d spinors. We identify the operators in d = 4−2 that correspond to the additional conserved currents at d = 3 and compute their infrared dimensions.

Scaling dimensions in QED3 from the ϵ-expansion

“…1 The one-loop result of ref. [18] led to the estimate N c f ≤ 2. Bilinear operators, i.e., operators with two fermion fields, are interesting because they are presumably among the operators with lowest dimension.…”

“…Indeed, as discussed in ref. [18], the one-loop approximation predicts that the lowest eigenvalue becomes relevant for N f < 3. The two-loop computation presented here changes this prediction.…”

“…This leads to the conjecture that their scaling dimension should approach the value ∆ = 2 as → 1 2 , which was tested at the one-loop level in ref. [18].…”

“…In particular, ref. [18] considered operators constructed out of gauge-invariant products of either four or two fermion fields.…”

“…When 1 we can access observables via a perturbative expansion in and subsequently attempt an extrapolation to = 1 2 . The -expansion of QED was employed to estimate scaling dimensions [18,19], the free energy F [20], and the coefficients C T and C J [14]. In particular, ref.…”