Black holes with topological charges in Chern-Simons AdS5 supergravity

We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in $$ \mathcal{N} $$ N = 4 Chern-Simons AdS5 supergravity. They are governed by three parameters associated to the mass, axial torsion and amplitude of the internal soliton, and two ones to the gravitational hair. They describe geometries that can be a global AdS space, naked singularity or a (non-)extremal black hole. We analyze physical properties of two inequivalent asymptotically AdS solutions when the spatial section at radial infinity is either a 3-sphere or a projective 3-space. An important feature of these 3-parametric solutions is that they possess a topological structure including two SU(2) solitons that wind nontrivially around the black hole horizon, as characterized by the Pontryagin index. In the extremal black hole limit, the solitons’ strengths match and a soliton-antisoliton system unwinds. That limit admits both non-BPS and BPS configurations. For the latter, the pure gauge and non-pure gauge solutions preserve 1/2 and 1/16 of the original supersymmetries, respectively. In a general case, we compute conserved charges in Hamiltonian formalism, finding many similarities with standard supergravity black holes.

Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear $$\sigma $$-model

In this paper, we construct the first analytic examples of $$(3+1)$$ ( 3 + 1 ) -dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the Einstein-SU(2) non-linear $$\sigma $$ σ -model. These gravitating topological solitons at a large distance from the axis look like a (boosted) cosmic string with an angular defect given by the parameters of the theory, and near the axis, the parameters of the solutions can be chosen so that the metric is singularity free and without angular defect. The curvature is concentrated on a tube around the axis. These solutions are similar to the Cohen–Kaplan global string but regular everywhere, and the non-linear $$\sigma $$ σ -model regularizes the gravitating global string in a similar way as a non-Abelian field regularizes the Dirac monopole. Also, these solutions can be promoted to those of the fully coupled Einstein–Maxwell non-linear $$\sigma $$ σ -model in which the non-linear $$\sigma $$ σ -model is minimally coupled both to the U(1) gauge field and to General Relativity. The analysis shows that these solutions behave as superconductors as they carry a persistent current even when the U(1) field vanishes. Such persistent current cannot be continuously deformed to zero as it is tied to the topological charge of the solutions themselves. The peculiar features of the gravitational lensing of these gravitating solitons are shortly discussed.

Washington units, semispecial units, and annihilation of class groups

Special units are a sort of predecessor of Euler systems, and they are mainly used to obtain annihilators for class groups. So one is interested in finding as many special units as possible (actually we use a technical generalization called “semispecial”). In this paper we show that in any abelian field having a real genus field in the narrow sense all Washington units are semispecial, and that a slightly weaker statement holds true for all abelian fields. The group of Washington units is very often larger than Sinnott’s group of cyclotomic units. In a companion paper we will show that in concrete families of abelian fields the group of Washington units is much larger than that of Sinnott units, by giving lower bounds on the index. Combining this with the present paper gives strong annihilation results.

Weyl doubling

We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space.We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions.For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

Non-Abelian Gravitoelectromagnetism and Applications at Finite Temperature

Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak-field approximation of the gravitation field. Here, a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects, some interesting physical phenomena are investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect at zero and finite temperatures for this non-abelian field are calculated.

Color structure of gluon field magnetic mass

The color structure of the gluon field magnetic mass is investigated in the lattice SU(2) gluodynamics. To realize that the interaction between a monopole–antimonopole string and external neutral Abelian chromomagnetic field flux is considered. The string is introduced in the way proposed by Srednicki and Susskind. The neutral Abelian field flux is introduced through the twisted boundary conditions. Monte Carlo simulations are performed on 4D lattices at finite temperature. It is shown that the presence of the Abelian field flux weakens the screening of the string field. That means decreasing the gluon magnetic mass for this environment. The contribution of the neutral Abelian field has the form of “enhancing” factor in the fitting functions. This behavior independently confirms the long-range nature of the neutral Abelian field reported already in the literature. The comparison with analytic calculations is given.