The Chiral and U(1)_A Symmetries of the QCD Phase Transition using Chiral Lattice Fermions

With regard to the nature of the finite-temperature QCD phase transition and the fate of the chiral and anomalous axial symmetries associated with it, we present in this thesis two parallel sets of investigations into the QCD phase transition region between 139 and 195 MeV. Both studies adopt the Iwasaki gauge action augmented with the dislocation suppression determinant ratio with 2+1 flavors of chiral fermions. This choice of lattice action accurately reproduces the SU(2)_L × SU(2)_R and U(1)_A symmtries of the continuum. The first study simulates QCD thermodynamics on a line of constant physics that represents 200 MeV pions and physical kaons using domain wall fermions (DWF) at three space-time volumes: 16³ × 8, 24³ × 8, and 32³ × 8, where the largest volume varies in linear size between 5.6 fm (at T = 139 MeV) and 4.0 fm (at T = 195 MeV). The chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum are reported and compared between different volumes as well as with the staggered results. We find a pseudo-critical temperature, T_c , of approximately 165 MeV and strong finite volume dependence below T_c. Clear evidence is seen for U(1)_A symmetry breaking above T_c which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation. The second study targets on a line of constant physics with pions of physical mass, which is the very first study using a chiral lattice fermion formulaation. We continue to use the basic setup from the m_π ≈ 200 MeV simulations, except that we use a generalized form of domain wall fermions, known as the M ̈bius fermions, to further reduce the residual chiral symmetry breaking present in the domain wall formulation with finite extent in the fifth dimension. Preliminary results including the chiral condensates and the susceptibilities are reported for two space-time volumes of 32³ × 8 and 64³ × 8. We observe a dramatic increase in the disconnected susceptibilities and a shift in the pseudo-critical temperature from 165 MeV to about 154 MeV, when the pion mass is decreased from 200 MeV to 135 MeV.