Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them

Abstract

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang-Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $X_0=1/2$ (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $X_0$ is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein-Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D'Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifest itself in a difference between the degeneracies of the corresponding energy levels.

arXiv comment18 pages, 9 figures

References in corpus (33)

• A Four Dimensional Generalization of the Quantum Hall Effect
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Non-Abelian BPS Monopoles in N=4 Gauged Supergravity
• Quantum Hall Effect in Higher Dimensions
• Gravitating Monopole Solutions II
• The Eight Dimensional Quantum Hall Effect and the Octonions
• Effective field theory description of the higher dimensional quantum Hall liquid
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• The effective action for edge states in higher dimensional quantum Hall systems
• Higher-Dimensional Quantum Hall Effect in String Theory
• Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model
• Quantum Hall effect on $S^3$, edge states and fuzzy $S^3/{\mathbf{Z}}_2$
• Non-commutative geometry of 4-dimensional quantum Hall droplet
• Confinement from Merons
• Spinning Gravitating Skyrmions
• Quantum Hall Effect on Higher Dimensional Spaces
• Geometric construction of the Quantum Hall Effect in all even dimensions
• Non-Abelian gravitating solitons with negative cosmological constant
• Exact meron Black Holes in four dimensional SU(2) Einstein-Yang-Mills theory
• Gravitational catalysis of merons in Einstein-Yang-Mills theory
• Dyons and dyonic black holes in $\mathfrak{su}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space-time
• Odd-Parity Negative Modes of Einstein-Yang-Mills Black Holes and Sphalerons
• Axially symmetric SU(3) Gravitating Skyrmions
• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Topological black holes in $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• Gravitating BPS Skyrmions
• The Entropy Function for the Black Holes of Nariai Class
• Gravitating gauged BPS baby Skyrmions
• Incompressible fluid inside an astrophysical black hole?

Cited by in corpus (2)

• Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density