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We find that competition between random Kondo and random magneticcorrelations results in a quantum phase transition from a local Fermi liquid toa spin liquid. The local charge susceptibility turns out to have exactly thesame critical exponent as the local spin susceptibility, suggesting novelduality between the Kondo singlet phase and the critical local moment statebeyond the Landau-Ginzburg-Wilson symmetry breaking framework. This leads us topropose an enhanced symmetry at the local quantum critical point, described byan O(4) vector for spin and charge. The symmetry enhancement serves mechanismof electron fractionalization in critical impurity dynamics, where suchfractionalized excitations are identified with topological excitations.

Novel duality in disorder driven local quantum criticality