Magnetic Vortex Lattices in Finite Isospin Chiral Perturbation Theory

We study finite isospin chiral perturbation theory ($\chi$PT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and $\chi$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $\chi$PT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.Comment: 9 pages, 4 figure

Mean-field theory of baryonic matter for QCD in the large NcN_{c} and heavy quark mass limits

We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large $N_c$ limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation with each of the quarks moving in an average potential due to the remaining quarks is heuristic. It is important to justify this heuristic description for the case of baryonic matter since systems of interacting baryons are intrinsically more complicated than single baryons due to the possibility of hidden color states---states in which the subsystems making up the entire baryon crystal are not color-singlet nucleons but rather colorful states coupled together to make a color-singlet state. In this work, we provide a formal justification of this heuristic prescription. In order to do this, we start by taking the heavy quark limit, thus effectively reducing the problem to a many-body quantum mechanical system. This problem can be formulated in terms of integrals over coherent states, which for this problem are simple Slater determinants. We show that for the many-body problem, the support region for these integrals becomes narrow at large $N_c$, yielding an energy which is well-approximated by a single coherent state---that is a mean-field description. Corrections to the energy are of relative order $1/N_c$. While hidden color states are present in the exact state of the heavy quark system, they only influence the interaction energy at sub-leading order in $1/N_{c}$.Comment: 9 page

On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.Comment: 12 pages, 1 tabl

Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to O(p6)\mathcal{O}(p^6) in a uniform magnetic field

We study three-flavor QCD in a uniform magnetic field using chiral perturbation theory ($\chi$PT). We construct the vacuum free energy density, quark condensate shifts induced by the magnetic field and the renormalized magnetization to $\mathcal{O}(p^6)$ in the chiral expansion. We find that the calculation of the free energy is greatly simplified by cancellations among two-loop diagrams involving charged mesons. In comparing our results with recent $2+1$-flavor lattice QCD data, we find that the light quark condensate shift at $\mathcal{O}(p^6)$ is in better agreement than the shift at $\mathcal{O}(p^4)$. We also find that the renormalized magnetization, due to its smallness, possesses large uncertainties at $\mathcal{O}(p^{6})$ due to the uncertainties in the low-energy constants.Comment: 23 pages, 3 sets of figures, matches published versio