Quantum Electrodynamics in d=3 from the ε Expansion.

Area of Science:

• Quantum Field Theory
• Condensed Matter Physics
• High Energy Physics

Background:

• Quantum electrodynamics in 3D (QED3) exhibits complex behavior depending on fermion flavor number (N_{f}).
• Chiral symmetry breaking is a key phenomenon in such theories for N_{f} below a critical value (N_{f}^{c}).

Purpose of the Study:

• To analyze the infrared (IR) behavior of QED3 using an epsilon expansion around d=4-2ε.
• To compute critical exponents and understand the role of fermion bilinear and quadrilinear operators.
• To investigate the enhanced symmetries in 3D spinors and their corresponding conserved currents.

Main Methods:

• Utilizing an epsilon expansion (d=4-2ε) to study the 3D conformal field theory.
• Perturbative calculations of infrared dimensions for fermion operators.
• Identifying operators corresponding to enhanced symmetries in 3D.

Main Results:

• The epsilon expansion provides estimates for the critical number of flavors (N_{f}^{c}).
• Quadrilinear operators can become relevant in the IR for small N_{f}, destabilizing the fixed point.
• The dimensions of operators associated with enhanced symmetries at d=3 were computed.

Conclusions:

• The study provides insights into the phase structure of QED3, particularly around the chiral symmetry breaking transition.
• The epsilon expansion is a viable tool for estimating N_{f}^{c} and understanding operator relevance.
• The enhanced symmetries in 3D QED3 and their associated conserved currents are characterized.