  The phase diagram of the Bose-Fermi Kondo model contains an SU(2)-invariant
Kondo-screened phase separated by a continuous quantum phase transition from a
Kondo-destroyed local moment phase. We analyze the effect of the Berry phase
term of the spin path integral on the quantum critical properties of this
quantum impurity model. For a range of the power-law exponent characterizing
the spectral density of the dissipative bosonic bath, neglecting the influence
of the Berry phase term makes the fixed point Gaussian. For the same range of
the spectral density exponent, incorporating the Berry phase term leads instead
to an interacting fixed point, for which a quantum to classical mapping breaks
down. Some general implications of our results are discussed.
