CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
Cuomo, A note on the large charge expansion in 4d CFT , Phys
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The analysis shows that analyticity bounds in Lorentz-broken theories require gapped excitations to propagate slower than gapless ones at low momenta relative to the mass gap.
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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Moduli Spaces in CFT: Large Charge Operators
CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
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IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
The analysis shows that analyticity bounds in Lorentz-broken theories require gapped excitations to propagate slower than gapless ones at low momenta relative to the mass gap.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.