  A quantum spin impurity coupled to a critical free field (the Bose-Kondo
model) can be represented as a 0+1D field theory with long-range-in-time
interactions that decay as $|t-t'|^{-(2-\delta)}$. This theory is a simpler
analogue of nonlinear sigma models with topological Wess-Zumino-Witten terms in
higher dimensions. In this note we show that the RG flows for the impurity
problem exhibit an annihilation between two nontrivial RG fixed points at a
critical value $\delta_c$ of the interaction exponent. The calculation is
controlled at large spin $S$. This clarifies the phase diagram of the
Bose-Kondo model and shows that it serves as a toy model for phenomena
involving fixed-point annihilation and "quasiuniversality" in higher
dimensions.
