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We describe the dynamics of a single fermion in a dispersionless band coupledto the 2+1 dimensional conformal field theory (CFT) describing the quantumphase transition of a bosonic order parameter with N components. The fermionicspectral functions are expected to apply to the vicinity of quantum criticalpoints in two-dimensional metals over an intermediate temperature regime wherethe Landau damping of the order parameter can be neglected. Some of our resultsare obtained by a mapping to an auxiliary problem of a CFT containing a defectline with an external field which locally breaks the global O(N) symmetry.

Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory