Phase structure of compactified SU(N)SU(N) gauge theories in magnetic backgrounds

We discuss the properties of non-abelian gauge theories formulated on manifolds with compactified dimensions and in the presence of fermionic fields coupled to magnetic backgrounds. We show that different phases may emerge, corresponding to different realizations of center symmetry and translational invariance, depending on the compactification radius and on the magnitude of the magnetic field. Our discussion focuses on the case of an $SU(3)$ gauge theory in 4 dimensions with fermions fields in the fundamental representation, for which we provide some exploratory numerical lattice results.Comment: 5 pages, 7 figure

Magnetic susceptibility and equation of state of N_f = 2+1 QCD with physical quark masses

We determine the free energy of strongly interacting matter as a function of an applied constant and uniform magnetic field. We consider N_f = 2+1 QCD with physical quark masses, discretized on a lattice by stout improved staggered fermions and a tree level improved Symanzik pure gauge action, and explore three different lattice spacings. For magnetic fields of the order of those produced in non-central heavy ion collisions (eB ~ 0.1 GeV^2) strongly interacting matter behaves like a medium with a linear response, and is paramagnetic both above and below the deconfinement transition, with a susceptibility which steeply rises in the deconfined phase. We compute the equation of state, showing that the relative increase in the pressure due to the magnetic field gets larger around the transition, and of the order of 10 % for eB ~ 0.1 GeV^2.Comment: 11 pages, 10 figures, 3 tables. Final version published in Physical Review

Magnetic Susceptibility of Strongly Interacting Matter across the Deconfinement Transition

We propose a method to determine the total magnetic susceptibility of strongly interacting matter by lattice QCD simulations, and present first numerical results for the theory with two light flavors, which suggest a weak magnetic activity in the confined phase and the emergence of strong paramagnetism in the deconfined, Quark-Gluon Plasma phase.Comment: 6 pages, 6 figures, 2 tables. Final version published in Physical Review Letter

Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields

We investigate two flavor QCD in presence of CP-odd electromagnetic background fields and determine, by means of lattice QCD simulations, the induced effective theta term to the first order in the scalar product of E and B. We employ a rooted staggered discretization and study lattice spacings down to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a positive measure, we consider purely imaginary electric fields and real magnetic fields, then exploiting analytic continuation. Our results are relevant to a description of the effective pseudoscalar QED-QCD interactions.Comment: 5 pages, 4 figures, 1 table. New data and references added. Matches the published versio

Anisotropy of the quark-antiquark potential in a magnetic field

We investigate the static $\overline{Q}Q$-potential for $N_f = 2+1$ QCD at the physical point in the presence of a constant and uniform external magnetic field. The potential is found to be anisotropic and steeper in the directions transverse to the magnetic field than in the longitudinal one. In particular, when compared to the standard case with zero background field, the string tension increases (decreases) in the transverse (longitudinal) direction, while the absolute value of the Coulomb coupling and the Sommer parameter show an opposite behavior.Comment: 6 pages, 5 figures, 1 table. Final published versio

Curvature of the chiral pseudo-critical line in QCD

We determine the curvature of the pseudo-critical line of strong interactions by means of numerical simulations at imaginary chemical potentials. We consider $N_f=2+1$ stout improved staggered fermions with physical quark masses and the tree level Symanzik gauge action, and explore two different sets of lattice spacings, corresponding to temporal extensions $N_t = 6$ and $N_t = 8$. Both the renormalized chiral condensate and the renormalized chiral susceptibility are used to locate the transition. The determinations obtained from the two quantities are in good agreement, a preliminary continuum extrapolation yields $\kappa = 0.013(2)(1)$. We also investigate the impact of a non-zero strange quark chemical potential and compare our results to previous determinations in the literature, discussing the possible sources of systematic errors affecting the various procedures.Comment: 16 pages, 12 figures, 11 tables. Published versio

Curvature of the chiral pseudo-critical line in QCD: continuum extrapolated results

We determine the curvature of the pseudo-critical line of strong interactions by means of numerical simulations at imaginary chemical potentials. We consider $N_f=2+1$ stout improved staggered fermions with physical quark masses and the tree level Symanzik gauge action, and explore four different sets of lattice spacings, corresponding to $N_t = 6,8,10,12$, in order to extrapolate results to the continuum limit. Our final estimate is $\kappa = 0.0135(20)$.Comment: 11 pages, 10 figures, 4 tables. Version to appear in Physical Review

Roberge-Weiss endpoint at the physical point of Nf=2+1N_f = 2+1 QCD

We study the phase diagram of $N_f = 2+1$ QCD in the $T - \mu_B$ plane and investigate the critical point corresponding to the onset of the Roberge-Weiss transition, which is found for imaginary values of $\mu_B$. We make use of stout improved staggered fermions and of the tree level Symanzik gauge action, and explore four different sets of lattice spacings, corresponding to $N_t = 4,6,8,10$, and different spatial sizes, in order to assess the universality class of the critical point. The continuum extrapolated value of the endpoint temperature is found to be $T_{\rm RW} = 208(5)$ MeV, i.e. $T_{\rm RW}/T_c \sim 1.34(7)$, where $T_c$ is the chiral pseudocritical temperature at zero chemical potential, while our finite size scaling analysis, performed on $N_t = 4$ and $N_t = 6$ lattices, provides evidence for a critical point in the $3d$ Ising universality class.Comment: 10 pages, 14 eps figures, 2 tables, final version published in Physical Review

QCD with external background fields

We discuss the non-perturbative properties of Quantum Chromodynamics in the presence of external background fields. In particular we study the effects of chemical potentials on the deconfinement transition, and the impact of magnetic fields on the static quark confining potential and on the Equation of State of strongly interacting matter