QCD-like theories at nonzero temperature and density

We investigate the properties of hot and/or dense matter in QCD-like theories with quarks in a (pseudo)real representation of the gauge group using the Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice spin model with nearest-neighbor interactions. We first keep our discussion as general as possible, and only later focus on theories with adjoint quarks of two or three colors. Calculating the phase diagram in the plane of temperature and quark chemical potential, it is qualitatively confirmed that the critical temperature of the chiral phase transition is much higher than the deconfinement transition temperature. At a chemical potential equal to half of the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC) phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is used to study the tetracritical behavior around the intersection point of the deconfinement and BEC transition lines, which are both of second order. We obtain a compact expression for the expectation value of the Polyakov loop in an arbitrary representation of the gauge group (for any number of colors), which allows us to study Casimir scaling at both nonzero temperature and chemical potential.Comment: JHEP class, 31 pages, 7 eps figures; v2: error in Eq. (3.11) fixed, two references added; matches published versio

Compact Stars - How Exotic Can They Be?

Strong interaction physics under extreme conditions of high temperature and/or density is of central interest in modern nuclear physics for experimentalists and theorists alike. In order to investigate such systems, model approaches that include hadrons and quarks in a unified approach, will be discussed. Special attention will be given to high-density matter as it occurs in neutron stars. Given the current observational limits for neutron star masses, the properties of hyperonic and hybrid stars will be determined. In this context especially the question of the extent, to which exotic particles like hyperons and quarks affect star masses, will be discussed.Comment: Contributon to conference "Nuclear Physics: Present and Future", held in Boppard (Germany), May 201

Lattice worldline representation of correlators in a background field

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.Comment: 54 pages, 14 figure

Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Universality of Phases in QCD and QCD-like Theories

We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.Comment: v1: 35 pages, 6 figures; v2: 37 pages, 6 figures, minor improvements, conclusion unchanged; v3: version published in JHE

Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model

In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD.Comment: 35 pages, 4 figures, v2: added comments about frequency-dependent conductivity at the end of section 4; references added; version to appear in JHE

Holographic chiral magnetic spiral

We study the ground state of baryonic/axial matter at zero temperature chiral-symmetry broken phase under a large magnetic field, in the framework of holographic QCD by Sakai-Sugimoto. Our study is motivated by a recent proposal of chiral magnetic spiral phase that has been argued to be favored against previously studied phase of homogeneous distribution of axial/baryonic currents in terms of meson super-currents dictated by triangle anomalies in QCD. Our results provide an existence proof of chiral magnetic spiral in strong coupling regime via holography, at least for large axial chemical potentials, whereas we don't find the phenomenon in the case of purely baryonic chemical potential.Comment: 24 pages, 15 figure

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

Anomaly and a QCD-like phase diagram with massive bosonic baryons

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-\mu_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly.Comment: 22 pages, 16 figures, 5 tables, references adde

Chiral perturbation theory in a magnetic background - finite-temperature effects

We consider chiral perturbation theory for SU(2) at finite temperature $T$ in a constant magnetic background $B$. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as between $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field. The increase of $T_c$ as a function of $B$ is in agreement with most model calculations but in disagreement with recent lattice calculations.Comment: 24 pages and 9 fig