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Quantum Field Theory Anomalies in Condensed Matter Physics
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Quantum Field Theory Anomalies in Condensed Matter Physics
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We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.
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Cited by 1 Pith paper
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Spin-charge deconfinement and emergent $\mathrm{AdS}_3$ structure from a self-consistent dressing of Fierz-complete $(1+1)$d Dirac fermions
A self-consistent dressing of Fierz-complete (1+1)d Dirac fermions yields spin-charge deconfinement diagnosed by Wilson loops, an emergent sl(2,R) gauge field, and an order-parameter manifold promoted to AdS3 ≅ SL(2,R).
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