Two dimensional many-body systems with a contact interaction have a SO(2,1) symmetry at the classical level.For two-dimensional (2D) atomic Fermi gases, including quantum effects, the SO(2,1) symmetry is broken explicitly via the contact correlation operator.Consequently the frequency of the breathing mode omega_B of the 2D Fermi gas in harmonic traps can be different from 2omega_0, with omega_0 the trapping frequency of harmonic potentials.At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for omega_B.We further calculate omega_B through the Euler equations in the hydrodynamic regime.The obtained value of omega_B satisfies the upper bounds and shows deviation from 2omega_0 which can be as large as about 8% [1].