Non-renormalization Theorem Originating in a New Fixed Point of the Vector Manifestation

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We study the pion velocity at the critical temperature of chiral symmetry restoration in QCD. Starting from the premise that the bare effective field theory is to be defined from the underlying QCD, we incorporate the effects of Lorentz non-invariance into the bare theory by matching an effective field theory to QCD at a suitable matching scale, and investigate how the Lorentz non-invariance existing in the bare theory influences physical quantities. Using the hidden local symmetry model as the effective field theory, where the chiral symmetry restoration is realized as the vector manifestation (VM), we find that the pion velocity at the critical temperature receives neither quantum nor (thermal) hadronic corrections at the critical temperature even when we start from the bare theory with Lorentz symmetry breaking. This is likely the manifestation of a new fixed point in the Lorentz non-invariant formulation of the VM.