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Quantum impurities serve as in-situ probes of the frustrated quantum magnets,and Dirac spin liquids are an important class of quantum spin liquids. Here, wepresent a general method, a combination of the Chern-Simons fermionization andthe Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spinliquids. Under the Chern-Simons fermionization, the gauge fluctuations areapparently suppressed and the low-energy physics is described by a number ofDirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)Deffective theory can be further reduced into the (1+1)D Wess-Zumino-Wittentheory by rotational symmetry, where the pseudospin-exchange between Diracfermions and the impurity can then be solved by the non-Abelian bosonization.Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified,respectively, depending on the relevance of the impurity scattering among theDirac valleys. This leads to experimental fingerprints for Dirac spin liquids,including a Kondo-induced magneto-thermal effect, a non-monotonous thermalconductivity during the crossover, and an anisotropic spin correlationfunction.

Kondo signatures in Dirac spin liquids: Non-Abelian bosonization after Chern-Simons fermionization