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Conformal field theories in a magnetic field
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We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs for a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge.
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Magnetised Bounds for Conformal Field Theories
Parity-invariant 3d CFTs gapped by a magnetic field satisfy c0 <= 0 and additional Wilson-coefficient bounds from dispersion relations, implying diamagnetism and positive background-monopole scaling dimensions.
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