Exact quantum scale invariance of three-dimensional reduced QED theories

David Dudal,Pablo Pais,Ana Júlia Mizher

doi:10.1103/physrevd.99.045017

Abstract

An effective quantum field theory description of graphene in the ultra-relativistic regime is given by reduced QED aka. pseudo QED aka. mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting CFT in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the b-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a non-supersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.

Highlights

Conformal invariance has played an important role in condensed matter physics and high energy physics since the 1980s, in particular after the ground breaking work in d 1⁄4 2 dimensions of [1] and its paramount relevance for string theory
It was investigated and proposed that mixed-dimensional quantum electrodynamics (QED) is another interacting conformal field theories (CFT) [5], see [6]. It arose in the context of new physics related to introducing a boundary into a CFT, in particular the appearance of extra boundary-related anomalous terms in the energymomentum trace/correlation functions, and the latter connection with the standard anomaly contributions
The precise nature of the gauge fixing choice will be of little concern in the current note. This version of mixed-dimensional QED, known as reduced QED (RQED3) or pseudo QED [10,11], already made its appearance in the literature before, as its physical relevance is motivated from condensed matter

Summary

Published by the American Physical Society

The precise nature of the gauge fixing choice will be of little concern in the current note This version of mixed-dimensional QED, known as reduced QED (RQED3) or pseudo QED [10,11], already made its appearance in the literature before, as its physical relevance is motivated from condensed matter. In [17], it was pointed out that ZA 1⁄4 1 as it concerns the renormalization of a non-local term in the free (quadratic) part of action, incompatible with the observation that counterterms must be local polynomials in the fields and derivatives thereof. This rationale was based on [33].

ATμ δμν

It is understood that