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We investigated the chiral symmetry and U_A(1) anomaly at finite temperatureby applying the functional renormalization group to the SU(3) linear sigmamodel. Expanding the local potential around the classical fields, we derivedthe flow equations for the renormalization parameters. In chiral limit, theflow equation for the chiral condensate is decoupled from the others and can beanalytically solved. The Goldstone theorem is guaranteed in vacuum and atfinite temperature, and the two phase transitions for the chiral and U_A(1)symmetry restoration happen at the same critical temperature. In general casewith explicit chiral symmetry breaking, the two symmetries are partially andslowly restored, and the scalar and pseudoscalar meson masses are controlled bythe restoration in the limit of high temperature.

Functional Renormalization for Chiral and U_A(1) Symmetries at Finite Temperature