We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm) 3 and (11 fm) 3 and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of Nt = 8. The disconnected chiral susceptibility, χ disc shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous cross-over for mπ = 135 MeV. The peak location determines a pseudo-critical temperature Tc = 155(1)(8) MeV. Chiral SU (2)L ×SU (2)R symmetry is fully restored above 164 MeV, but anomalous U (1)A symmetry breaking is non-zero above Tc and vanishes as T is increased to 196 MeV.PACS numbers: 11.15. Ha, 12.38.Gc As the temperature of the QCD vacuum is increased above the QCD energy scale Λ QCD = 300 MeV, asymptotic freedom implies that the vacuum breaking of chiral symmetry must disappear and the familiar chirally-asymmetric world of massive nucleons and light pseudoGoldstone bosons must be replaced by an SU (2) L × SU (2) R symmetric plasma of nearly massless up and down quarks and gluons. Predicting, observing and characterizing this transition has been an experimental and theoretical goal since the 1980's. General principles are consistent with this being either a first-order transition for sufficiently light pion mass or a second-order transition in the O(4) universality class at zero pion mass with cross-over behavior for non-zero m π . While second order behavior is commonly expected, first-order behavior may be more likely if anomalous U (1) A symmetry is partially restored at T c resulting in an effectiveThe importance of the SU (2) L × SU (2) R chiral symmetry of QCD for the phase transition has motivated the widespread use of staggered fermions in lattice studies of QCD thermodynamics because this formulation possesses one exact chiral symmetry at finite lattice spacing, broken only by the quark mass. However, the flavor symmetry of the staggered fermion formulation is complicated showing an SU L (4) × SU R (4) "taste" symmetry that is broken by lattice artifacts and made to resemble the physical SU (2) L × SU (2) R symmetry by taking the square root of the Dirac determinant, a procedure believed to have a correct but subtle continuum limit for non-zero quark masses.

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: 24 3 × 8 and 32 3 × 8, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, 16 3 ×8 volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the SU (2) L × SU (2) R and U (1) A symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, T c , of approximately 165 MeV consistent with previous results 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.

One intriguing beyond-the-Standard-Model particle is the QCD axion, which could simultaneously provide a solution to the Strong CP problem and account for some, if not all, of the dark matter density in the universe. This particle is a pseudo-Nambu-Goldstone boson of the conjectured Peccei-Quinn (PQ) symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry breaking scale, f a , whose value is roughly greater than 10 9 GeV (or, conversely, the axion mass, m a , is roughly less than 10 4 µeV). The density of axions in the universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early-universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the CP-violating phase, θ. However, this quantity is generically non-perturbative and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small θ from firstprinciple lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the universe, which is required to be less than or equal to the dark matter density. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-θ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound m a ≥ (14.6 ± 0.1) µeV when PQ-breaking occurs after inflation.

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U (1) A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N τ = 8 and spatial extent N σ = 16 in a temperature range of T = 139 − 195 MeV, corresponding to lattice spacings of a ≈ 0.12 − 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m π = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U (1) A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U (1) A and chiral symmetry restoration via Banks-Casher relations.

A new method of employing an isospin chemical potential for QCD-like theories with different number of colors, number of fermion flavors, and in different fermion representations is proposed.The isospin chemical potential, which can be simulated on the lattice due to its positive definite determinant gives a means to probe both confining theories and IR conformal theories without adjusting the lattice spacing and size. As the quark mass is reduced, the isospin chemical potential provides an avenue to extract the chiral condensate in confining theories through the resulting pseudoscalar condensate. For IR conformal theories, the mass anomalous dimension can be extracted in the conformal window through "finite density" scaling since the isospin chemical potential is coupled to a conserved current. In both of these approaches, the isospin chemical potential can be continuously varied for each ensemble at comparable costs while maintaining the hierarchy between the lattice size and lattice spacing. In addition to exploring these methods, finite volume and lattice spacing effects are investigated.