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Hund metals have attracted attention in recent years due to theirunconventional superconductivity, which supposedly originates fromnon-Fermi-liquid (NFL) properties of the normal state. When studying Hundmetals using dynamical mean-field theory, one arrives at a self-consistent"Hund impurity problem" involving a multiorbital quantum impurity with nonzeroHund coupling interacting with a metallic bath. If its spin and orbital degreesof freedom are screened at different energy scales, $T_\mathrm{sp} <T_\mathrm{orb}$, the intermediate energy window is governed by a novel NFLfixed point, whose nature had not yet been clarified. We resolve this problemby providing an analytical solution of a paradigmatic example of a Hundimpurity problem, involving two spin and three orbital degrees of freedom. Tothis end, we combine a state-of-the-art implementation of the numericalrenormalization group, capable of exploiting non-Abelian symmetries, with ageneralization of Affleck and Ludwig's conformal field theory (CFT) approachfor multichannel Kondo models. We characterize the NFL fixed point of Hundmetals in detail for a Kondo model with an impurity forming anSU(2)$\times$SU(3) spin-orbital multiplet, tuned such that the NFL energywindow is very wide. The impurity's spin and orbital susceptibilities thenexhibit striking power-law behavior, which we explain using CFT arguments. Wefind excellent agreement between CFT predictions and numerical renormalizationgroup results. Our main physical conclusion is that the regime of spin-orbitalseparation, where orbital degrees of freedom have been screened but spindegrees of freedom have not, features anomalously strong local spinfluctuations: the impurity susceptibility increases as$\chi_\mathrm{sp}^\mathrm{imp} \sim \omega^{-\gamma}$, with $\gamma > 1$.

Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)$\times$SU(3) Spin-Orbital Kondo Model