Electromagnetic current correlations in reduced quantum electrodynamics

Abstract

We consider a theory of massless reduced quantum electrodynamics (RQED$_{d_\gamma,d_e}$), e.g., a quantum field theory where the U(1) gauge field lives in $d_\gamma$-spacetime dimensions while the fermionic field lives in a reduced spacetime of $d_e$ dimensions ($d_e \leqslant d_\gamma$). In the case where $d_\gamma=4$ such RQEDs are renormalizable while they are super-renormalizable for $d_\gamma <4$. The 2-loop electromagnetic current correlation function is computed exactly for a general RQED$_{d_\gamma,d_e}$. Focusing on RQED$_{4,3}$, the corresponding $\beta$-function is shown to vanish which implies the scale invariance of the theory. Interaction correction to the 1-loop vacuum polarization, $\Pi_1$, of RQED$_{4,3}$ is found to be: $\Pi = \Pi_1 (1 + 0.056 \al)$ where $\al$ is the fine structure constant. The scaling dimension of the fermion field is computed at 1-loop and is shown to be anomalous for RQED$_{4,3}$.Comment: (v2) Accepted for publication in PRD. Conclusion and references added (some / referee's comments). No change in results. 8 pages, 3 figures. (v1) LaTeX file with feynMF package. 8 pages, no figur

On non-supersymmetric conformal manifolds: field theory and holography

“…11 In the context of boundary conformal field theories (bCFT) there also exist examples. One such example, the mixed dimensional QED discussed in [29,30], is even believed to admit a (perturbative-stable) conformal manifold. We thank Chris Herzog for making us aware of this possibility.…”

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in the Landau gauge

“…The multi-loop structure of the latter has been recently explored in Refs. [31,32]. With the help of the ansatz (9), one can then see that the r.h.s.…”

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

“…where the gauge dependence comes from the fact that we work in a non-local gauge andΠ arises from the twoloop polarization operator in dimension D = 3 [30,40,41] which may be graphically represented as:…”

“…One difference is that the gauge fixing parameter in reduced QED is twice less than the one in QED 3 . Such a difference can be taken into account with the help of our present results for QED 3 together with the multi-loop results obtained in [30,31]. The case of reduced QED, and its relation with dynamical gap generation in graphene which is the subject of active ongoing research, see, e.g., the reviews [32,33], will be considered in a separate paper [34].…”