BCS theory of hadronic matter at high densities

The equilibrium between the so-called 2SC and CFL phases of strange quark matter at high densities is investigated in the framework of a simple schematic model of the NJL type. Equal densities are assumed for quarks $u,d$ and $s$. The 2SC phase is here described by a color-flavor symmetric state, in which the quark numbers are independent of the color-flavor combination. In the CFL phase the quark numbers depend on the color-flavor combination, that is, the number of quarks associated with the color-flavor combinations $ur,dg,sb$ is different from the number of quarks associated with the color flavor combinations $ug,ub,dr,db,sr,sg$. We find that the 2SC phase is stable for a chemical potential $\mu$ below $\mu_c=0.505$ GeV, while the CFL phase is stable above, the equilibrium pressure being $P_c=0.003$ GeV$^4$. We have used a 3-momentum regularizing cutoff $\Lambda=0.8$ GeV, which is somewhat larger than is usual in NJL type models. This should be adequate if the relevant chemical potential does not exceed 0.6 GeV.Comment: 6 figures, 13 page

Non-Abelian discrete gauge symmetries in 4d string models

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples.Comment: 58 pages; minor typos corrected and references adde

Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.Comment: Latex, 39 pages, 5 figure

Anomalies in Superfluids and a Chiral Electric Effect

We analyze the chiral transport terms in relativistic superfluid hydrodynamics. In addition to the spontaneously broken symmetry current, we consider an arbitrary number of unbroken symmetries and extend the results of arXiv:1105.3733. We suggest an interpretation of some of the new transport coefficients in terms of chiral and gravitational anomalies. In particular, we show that with unbroken gauged charges in the system, one can observe a chiral electric conductivity - a current in a perpendicular direction to the applied electric field. We present a motivated proposal for the value of the associated transport coefficient, linking it to the triangle anomaly. Along the way we present new arguments regarding the interpretation of the anomalous transport coefficients in normal fluids. We propose a natural generalization of the chiral transport terms to the case of an arbitrary number of spontaneously broken symmetry currents.Comment: 30 pages; v2: Onsager-relations argument corrected, references added; v3: fixed missing line in eq. (38

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

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

The sign problem across the QCD phase transition

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.Comment: 9 pages and 9 fig

Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD

We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with nonzero chemical potential. We explore a method to suppress the sign fluctuations of the Dirac determinant in the hadronic phase; the method employs a re-summation of gauge configurations that are related to each other by center transformations. We numerically test this method in two dimensions, and find that it successfully solves the silver-blaze problem. We analyze the system further, and measure its free energy F, the average phase theta of its Dirac determinant, and its chiral condensate . We show that F and are independent of mu in the hadronic phase but that, as chiral perturbation theory predicts, the quenched chiral condensate drops from its mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of theta qualitatively agrees with further, more recent, predictions from chiral perturbation theory.Comment: 43 pages, 17 figure

Reaction rates and transport in neutron stars

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.