Baryons and baryonic matter in the large Nc and heavy quark limits

This paper explores properties of baryons and finite density baryonic matter in an artificial world in which Nc, the number of colors, is large and the quarks of all species are degenerate and much larger than {\Lambda}_QCD. It has long been known that in large Nc QCD, baryons composed entirely of heavy quarks are accurately described in the mean-field approximation. However, the detailed properties of baryons in the combined large Nc and heavy quark limits have not been fully explored. Here some basic properties of baryons are computed using a variational approach. At leading order in both the large Nc and heavy quark expansions the baryon mass is computed explicitly as is the baryon form factor. Baryonic matter, the analog of nuclear matter in this artificial world, should also be well described in the mean-field approximation. In the special case where all baryons have an identical spin flavor structure, it is shown that in the formal heavy quark and large Nc limit interactions between baryons are strictly repulsive at low densities. The energy per baryon is computed in this limit and found to be exponentially small. It is shown that when the restriction to baryons with an identical spin-flavor structure is dropped, a phase of baryonic matter exists with a density of 2Nf times that for the restricted case but with the same energy (where Nf is the number of degenerate flavors). It is shown that this phase is at least metastable.Comment: 19 page

Is There a Peccei-Quinn Phase Transition?

The nature of axion cosmology is usually said to depend on whether the Peccei-Quinn (PQ) symmetry breaks before or after inflation. The PQ symmetry itself is believed to be an accident, so there is not necessarily a symmetry during inflation at all. We explore these issues in some simple models, which provide examples of symmetry breaking before and after inflation, or in which there is no symmetry during inflation and no phase transition at all. One effect of these observations is to relax the constraints from isocurvature fluctuations due to the axion during inflation. We also observe new possibilities for evading the constraints due to cosmic strings and domain walls, but they seem less generic.Comment: 14 pages. Several references adde

Ultraviolet singularities in classical brane theory

We construct for the first time an energy-momentum tensor for the electromagnetic field of a p-brane in arbitrary dimensions, entailing finite energy-momentum integrals. The construction relies on distribution theory and is based on a Lorentz-invariant regularization, followed by the subtraction of divergent and finite counterterms supported on the brane. The resulting energy-momentum tensor turns out to be uniquely determined. We perform the construction explicitly for a generic flat brane. For a brane in arbitrary motion our approach provides a new paradigm for the derivation of the, otherwise divergent, self-force of the brane. The so derived self-force is automatically finite and guarantees, by construction, energy-momentum conservation.Comment: 41 pages, no figures, minor change

Symmetric Skyrmions

We present candidates for the global minimum energy solitons of charge one to nine in the Skyrme model, generated using sophisticated numerical algorithms. Assuming the Skyrme model accurately represents the low energy limit of QCD, these configurations correspond to the classical nuclear ground states of the light elements. The solitons found are particularly symmetric, for example, the charge seven skyrmion has icosahedral symmetry, and the shapes are shown to fit a remarkable sequence defined by a geometric energy minimization (GEM) rule. We also calculate the energies and sizes to within at least a few percent accuracy. These calculations provide the basis for a future investigation of the low energy vibrational modes of skyrmions and hence the possibility of testing the Skyrme model against experiment.Comment: latex, 9 pages, 1 figure (fig1.gif

Twisted Vortices in a Gauge Field Theory

We inspect a particular gauge field theory model that describes the properties of a variety of physical systems, including a charge neutral two-component plasma, a Gross-Pitaevskii functional of two charged Cooper pair condensates, and a limiting case of the bosonic sector in the Salam-Weinberg model. It has been argued that this field theory model also admits stable knot-like solitons. Here we produce numerical evidence in support for the existence of these solitons, by considering stable axis-symmetric solutions that can be thought of as straight twisted vortex lines clamped at the two ends. We compute the energy of these solutions as a function of the amount of twist per unit length. The result can be described in terms of a energy spectral function. We find that this spectral function acquires a minimum which corresponds to a nontrivial twist per unit length, strongly suggesting that the model indeed supports stable toroidal solitons.Comment: 10 pages, 5 figures, title changed, minor revisions, and more references adde

Dual neutral variables and knot solitons in triplet superconductors

In this paper we derive a dual presentation of free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows one in particular to conclude that spin-triplet superconductors allow formation of stable finite-length closed vortices (the knotted solitons).Comment: Replaced with version published in PRL (added a discussion of the effect of the coupling of the fields {\vec s} and {\vec C} on knot stability). Latest updates of the paper and miscellaneous links related to knotted solitons are also available at the homepage of the author http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knotted solitons by Hietarinta and Salo are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mp

Numerical simulations of fragmentation of the Affleck-Dine condensate

We present numerical simulations of fragmentation of the Affleck-Dine condensate in two spatial dimensions. We argue analytically that the final state should consist of both Q-balls and anti-Q-balls in a state of maximum entropy, with most of the balls small and relativistic. Such a behaviour is found in simulations on a 100x100 lattice with cosmologically realistic parameter values. During fragmentation process, we observe filament-like texture in the spatial distribution of charge. The total charge in Q-balls is found to be almost equal to the charge in anti-Q-balls and typically orders of magnitude larger than charge asymmetry. Analytical considerations indicate that, apart from geometrical factors, the results of the simulated two dimensional case should apply also to the fully realistic three dimensional case.Comment: 28 pages, 39 figure

Hopf instantons in Chern-Simons theory

We study an Abelian Chern-Simons and Fermion system in three dimensions. In the presence of a fixed prescribed background magnetic field we find an infinite number of fully three-dimensional solutions. These solutions are related to Hopf maps and are, therefore, labelled by the Hopf index. Further we discuss the interpretation of the background field.Comment: one minor error corrected, discussion of gauge fixing added, some references adde

Constraints on Axion Models from K+→π+aK^+\to\pi^+ a

We explore a new class of axion models in which some, but not all, of the left-handed quarks have a Peccei-Quinn symmetry. These models are potentially afflicted by flavour changing neutral currents. We derive the bounds on the Peccei-Quinn symmetry-breaking scale from bounds on the $K^+\to \pi^+ a$ branching ratio, showing that in some cases they are even stronger than the astrophysical ones, but still not strong enough to kill off the models.Comment: 15pp RevTeX, 1 eps fig, uses graphics style. Expanded discussion on massive scalars and pseudoscalars, typos. To appear in Physical Review

Axion Radiation from Strings

This paper revisits the problem of the string decay contribution to the axion cosmological energy density. We show that this contribution is proportional to the average relative increase when axion strings decay of a certain quantity $N_{\rm ax}$ which we define. We carry out numerical simulations of the evolution and decay of circular and non-circular string loops, of bent strings with ends held fixed, and of vortex-antivortex pairs in two dimensions. In the case of string loops and of vortex-antivortex pairs, $N_{\rm ax}$ decreases by approximately 20%. In the case of bent strings, $N_{\rm ax}$ remains constant or increases slightly. Our results imply that the string decay contribution to the axion energy density is of the same order of magnitude as the well-understood contribution from vacuum realignment.Comment: 29 pages, 10 figure