In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal ...coupling with the Maxwell U(1) gauge field can be taken explicitly into account. The first approach (which is related to the generalization of the usual spherical hedgehog ansatz to situations without spherical symmetry at a finite Baryon density) allows for the construction of ordered arrays of Baryonic tubes and layers. When the minimal coupling of the Pions to the U(1) Maxwell gauge field is taken into account, one can show that the electromagnetic field generated by these inhomogeneous Baryonic condensates is of a force-free type (in which the electric and magnetic components have the same size). Thus, it is natural to wonder whether it is also possible to analytically describe magnetized hadronic condensates (namely, Hadronic distributions generating only a magnetic field). The idea of the second approach is to construct a novel BPS bound in the low-energy limit of QCD using the theory of the Hamilton–Jacobi equation. Such an approach allows us to derive a new topological bound which (unlike the usual one in the Skyrme model in terms of the Baryonic charge) can actually be saturated. The nicest example of this phenomenon is a BPS magnetized Baryonic layer. However, the topological charge appearing naturally in the BPS bound is a non-linear function of the Baryonic charge. Such an approach allows us to derive important physical quantities (which would be very difficult to compute with other methods), such as how much one should increase the magnetic flux in order to increase the Baryonic charge by one unit. The novel results of this work include an analysis of the extension of the Hamilton–Jacobi approach to the case in which Skyrme coupling is not negligible. We also discuss some relevant properties of the Dirac operator for quarks coupled to magnetized BPS layers.
In this article, we extend the strong deflection limit to calculate the deflection angle for a class of geometries which are asymptotically locally flat. In particular, we study the deflection of ...light in the surroundings of spherical black holes in Einstein–Skyrme theory. We find the deflection angle in this limit, from which we obtain the positions and the magnifications of the relativistic images. We compare our results with those corresponding to the Schwarzschild and the global monopole (Barriola–Vilenkin) spacetimes.
A
bstract
In this paper, we analyze the static solutions for the U(1)
4
consistent truncation of the maximally supersymmetric gauged supergravity in four dimensions. Using a new parametrization of ...the known solutions it is shown that for fixed charges there exist three possible black hole configurations according to the pattern of symmetry breaking of the (scalars sector of the) Lagrangian. Namely a black hole without scalar fields, a black hole with a primary hair and a black hole with a secondary hair respectively. This is the first, exact, example of a black hole with a primary scalar hair, where both the black hole and the scalar fields are regular on and outside the horizon. The configurations with secondary and primary hair can be interpreted as a spontaneous symmetry breaking of discrete permutation and reflection symmetries of the action. It is shown that there exist a triple point in the thermodynamic phase space where the three solution coexist. The corresponding phase transitions are discussed and the free energies are written explicitly as function of the thermodynamic coordinates in the uncharged case. In the charged case the free energies of the primary hair and the hairless black hole are also given as functions of the thermodynamic coordinates.
We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled ...differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed position in space.
The Casimir effect is a remarkable macroscopic feature of QED, while recent lattice studies have also shown its potential nontrivial consequences in QCD. In light of having a better understanding of ...the Casimir effect, it is advantageous to have a self-contained path integral formulation of the phenomenon. I will show how the Casimir effect between two uncharged plates in the presence of a chiral medium, modeled with an axion term
θF͂
μv
F
μv
, can be formulated in terms of the path integral, and how such a formulation leads to a 3D effective action of the restricted electromagnetic field.
A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least ...small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.
I analyze the quantum mechanical scattering off a topological defect (such as a Dirac monopole) as well as a Yukawa-like potential(s) representing the typical effects of strong interactions. This ...system, due to the presence of a short-range potential, can be analyzed using the powerful technique of the complex angular momenta which, so far, has not been employed in the presence of monopoles (nor of other topological solitons). Due to the fact that spatial spherical symmetry is achieved only up to internal rotations, the partial wave expansion becomes very similar to the Jacob-Wick helicity amplitudes for particles with spin. However, since the angular-momentum operator has an extra “internal” contribution, fixed cuts in the complex angular momentum plane appear. Correspondingly, the background integral in the Regge formula does not decrease for large values of |cosθ| (namely, large values of the Mandelstam variable s). Hence, the experimental observation of this kind of behavior could be a direct signal of nontrivial topological structures in strong interactions. The possible relations of these results with the soft Pomeron are shortly analyzed.
We construct exact, regular and topologically nontrivial configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear SU(2) field is regular ...everywhere and circumvents Derrick’s theorem because it depends explicitly on time, but in such a way that its energy-momentum tensor is compatible with a stationary metric. Moreover, the SU(2) configuration cannot be continuously deformed to the trivial Pion vacuum as it possesses a nontrivial winding number. We reduce the full coupled four-dimensional Einstein nonlinear sigma model system to a single second order ordinary differential equation. When the cosmological constant vanishes, such a master equation can be further reduced to an Abel equation. Two interesting regular solutions correspond to a stationary traversable wormhole (whose only “exotic matter” is a negative cosmological constant) and a (3+1)-dimensional cylinder whose (2+1)-dimensional section is a Lorentzian squashed sphere. The Klein-Gordon equation in these two families of spacetimes can be solved in terms of special functions. The angular equation gives rise to the Jacobi polynomials while the radial equation belongs to the Poschl-Teller family. The solvability of the Poschl-Teller problem implies nontrivial quantization conditions on the parameters of the theory.
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