Fixed point annihilation for a spin in a fluctuating field

Understand

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 $S$.