Scaling dimensions in \(\mathrm{QED}_{3}\) from the \(\epsilon\)-expansion. (English) Zbl 1383.81203
Summary: We study the fixed point that controls the IR dynamics of QED in \(d =4 - 2\epsilon\) dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the \(\epsilon\)-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to \(d=3\) to estimate their value at the IR fixed point of \(\mathrm{QED}_{3}\) as function of the number of fermions \(N_f\). The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of \(N_f\), which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the -expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of \(N_f\).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
Software:
FORMReferences:
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