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The $ϵ$ -expansion for QED

L. Di Pietro

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel

E-mail Address: lorenzo.dipietro@weizmann.ac.il

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Z. Komargodski

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel

E-mail Address: zohar.komargodski@weizmann.ac.il

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I. Shamir

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel

E-mail Address: itamar.shamir@weizmann.ac.il

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E. Stamou

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel

E-mail Address: emmanuel.stamou@weizmann.ac.il

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https://doi.org/10.1142/S0217751X16450391Cited by:0 (Source: Crossref)

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 $N_{f}^{c}$ . For $N_{f} \leq N_{f}^{c}$ , chiral symmetry breaking is believed to take place. In analogy with the Wilson-Fisher description of the critical $O (N)$ models in $d = 3$ , we use the existence of a fixed point in $d = 4 - 2 ϵ$ to study the three-dimensional theory. We show how the $ϵ$ -expansion can be used to study the anomalous dimension of 2- and 4-fermion operators. The latter leads to an estimate of the critical number $N_{f}^{c}$ . An important novelty compared to the $O (N)$ models is that, because of the structure of spinors, the theory in $d = 3$ has an enhanced symmetry. We identify the operators in $d = 4 - 2 ϵ$ that correspond to the additional conserved currents at $d = 3$ .

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The ϵ<math altimg="eq-00001.gif" display="inline"><mi>ϵ</mi></math>-expansion for QED

Abstract

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The $ϵ$ -expansion for QED