Analytic solutions in the gauged skyrme model and conservation laws in gauge theories with applications to black hole mechanics.
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Date
2021
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Publisher
Universidad de Concepción.
Abstract
The present thesis consists of two parts. Part I is devoted to the construction of
the first analytic examples of topologically non-trivial solutions of the U(1) gauged
Skyrme model within a finite box in (3 + 1)-dimensional flat space-time. There are
two types of gauged solitons. The first type corresponds to gauged Skyrmions living
within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the U(1) gauged Skyrme model whose periodic time-dependence is protected
by a winding number). The notion of electromagnetic duality can be extended for
these two types of configurations in the sense that some of the electric and magnetic
field components can be interchanged. These analytic solutions show very explicitly
the Callan-Witten mechanism (according to which magnetic monopoles may “swallow” part of the topological charge of the Skyrmion) since the electromagnetic field
contribute directly to the topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged
Skyrmions. On the other hand, the electric field is strongly suppressed in the centre
of gauged time crystals.
Part II is concerned with studying a new derivation of surface charges in gauge
theories. Part of the focus is on reviewing the method to compute quasi-local surface
charges for gauge theories to clarify conceptual issues and their range of applicabil ity. The surface charges found are quasi-local, explicitly coordinate independent, and
gauge invariant. Many surface charge formulas for gravity theories are expressed in
metric, tetrads-connection, and even Chern-Simons connection. For most of them,
the language of differential forms is exploited and contrasted with the more popular metric components language. The study focuses on General Relativity theory
coupled with matter fields as Maxwell, Skyrme, and spinors. To derive the sur face charges, we specify the phase space by identifying the symplectic structure.
We use the formulation of the covariant phase space method. Here the symplectic
structure has two parts: the standard Lee-Wald term plus a contribution from the
boundary term read from the action. The latter is fixed by requiring the on-shell
and linearized equations of motion condition, and exact symmetry condition. These
conditions guarantees the conservation of the symplectic structure in phase space,
and leads to the new concept of “symplectic symmetry”. Given the “conservation
law” satisfying the symplectic structure, we construct the corresponding charges,
the “symplectic symmetry generators”. The explicit expression of the charges corresponds to a function over the phase space.
We find the remarkable property that, in contrast with usual Noether procedures to
compute charges, the boundary terms and even topological terms do not affect the
surface charges. On the other hand, by studying two concrete examples, we also examine how torsion affects the surface charges. Both of them conclude that the torsion
field does not affect the general formula for the surface charges. Furthermore, three
examples with ready-to-download Mathematica notebook codes show the method in
full action. The charges and their associated first law of thermodynamics are derived
for: the BTZ black hole, the charged rotating (3 + 1)-black hole, and the Lorentzian
rotating Taub-NUT space-time.
Description
Tesis para postular al grado académico de Doctor en Ciencias Físicas.
Keywords
Campos de Calibre (Física), Modelo Skyrme, Campos Electromagnéticos