On the chiral perturbation theory for two-flavor two-color QCD at finite chemical potential

We construct the chiral perturbation theory for two-color QCD with two quark flavors as an effective theory on the SO(6)/SO(5) coset space. This formulation turns out to be particularly useful for extracting the physical content of the theory when finite baryon and isospin chemical potentials are introduced, and Bose--Einstein condensation sets on.Comment: 10 pages, 1 eps figure, to be published in Mod. Phys. Lett.

A model of flavors

We argue in favor of dynamical mass generation in an SU(2)xU(1) electroweak model with two complex scalar doublets with ordinary masses. The masses of leptons and quarks are generated by ultraviolet-finite non-perturbative solutions of the Schwinger-Dyson equations for full fermion propagators with self-consistently modified scalar boson exchanges. The W and Z boson masses are expressed in terms of spontaneously generated fermion proper self-energies in the form of sum rules. The model predicts two charged and four real neutral heavy scalars.Comment: 5 pages, REVTeX4, 5 feynmp figure

Gauged Wess-Zumino terms for a general coset space

The low-energy physics of systems with spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It has been known for half a century how to construct invariant Lagrangian densities for the low-energy effective theory of Nambu-Goldstone bosons. Contributions, invariant only up to a surface term -- also known as the Wess-Zumino (WZ) terms -- are more subtle, and as a rule are topological in nature. Although WZ terms have been studied intensively in theoretically oriented literature, explicit expressions do not seem to be available in sufficient generality in a form suitable for practical applications. Here we construct the WZ terms in $d=1,2,3,4$ spacetime dimensions for an arbitrary compact, semisimple and simply connected symmetry group $G$ and its arbitrary connected unbroken subgroup $H$, provided that the $d$-th homotopy group of the coset space $G/H$ is trivial. Coupling to gauge fields for the whole group $G$ is included throughout the construction. We list a number of explicit matrix expressions for the WZ terms in four spacetime dimensions, including those for QCD-like theories, that is vector-like gauge theories with fermions in a complex, real or pseudoreal representation of the gauge group.Comment: 19 pages; v2: the examples section substantially rewritten (a critical error corrected and a new example added), matches text to appear in Nucl. Phys.

Phase diagram of two-color quark matter at nonzero baryon and isospin density

We investigate the properties of cold dense quark matter composed of two colors and two flavors of light quarks. In particular, we perform the first model calculation of the full phase diagram at nonzero baryon and isospin density, thus matching the model-independent predictions of chiral perturbation theory at low density to the conjectured phase structure at high density. We confirm the presence of the Fulde-Ferrell (FF) phase in the phase diagram and study its dependence on the tunable parameter in the Lagrangian that simulates the effects of the quantum axial anomaly. As a byproduct, we clarify the calculation of the thermodynamic potential in the presence of the FF pairing, which was previously based on an ad hoc subtraction of an unphysical cutoff artifact. Furthermore, we argue that close to the diquark (or pion) Bose-Einstein condensation transition, the system behaves as a dilute Bose gas so that our simple fermionic model in the mean-field approximation is not quantitatively adequate. We suggest that including thermal fluctuations of the order parameter for Bose-Einstein condensation is crucial for understanding available lattice data.Comment: 14 pages, REVTeX4-1, 7 eps figures; v2: minor modifications + references added; version to be published in Phys. Rev.

Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields

Using a model-independent low-energy effective field theory, we calculate the free energy of three-dimensional antiferromagnets in a combination of mutually perpendicular external magnetic and staggered fields at the next-to-next-to-leading, two-loop order. Renormalization is carried out analytically, and the renormalization group invariance of the result is checked explicitly. The free energy is thus expressed solely in terms of temperature, the external fields, and a set of low-energy coupling constants, to be determined by experiment or by matching to the microscopic model of a given concrete material.Comment: 19 page

Linear sigma model at finite density in the 1/N expansion to next-to-leading order

We study relativistic Bose-Einstein condensation at finite density and temperature using the linear sigma model in the one-particle-irreducible 1/N-expansion. We derive the effective potential to next-to-leading (NLO) order and show that it can be renormalized in a temperature-independent manner. As a particular application, we study the thermodynamics of the pion gas in the chiral limit as well as with explicit symmetry breaking. At nonzero temperature we solve the NLO gap equation and show that the results describe the chiral-symmetry-restoring second-order phase transition in agreement with general universality arguments. However, due to nontrivial regularization issues, we are not able to extend the NLO analysis to nonzero chemical potential.Comment: 12 pages, REVTeX4, 6 eps figures; v2: added references + minor corrections throughout the text; version to appear in Phys. Rev.