908 research outputs found
Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry
We address the issue why Calabi-Yau manifolds exist with a mirror pair. We
observe that the irreducible spinor representation of the Lorentz group Spin(6)
requires us to consider the vector spaces of two-forms and four-forms on an
equal footing. The doubling of the two-form vector space due to the Hodge
duality doubles the variety of six-dimensional spin manifolds. We explore how
the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the
gauge theory formulation of six-dimensional Riemannian manifolds, we show that
the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian
Yang-Mills equations on the Calabi-Yau manifold. Therefore the mirror symmetry
of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian
Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory
perspective.Comment: v5; 49 pages, version to appear in Advances in High Energy Physic
Applications of hidden symmetries to black hole physics
This work is a brief review of applications of hidden symmetries to black
hole physics. Symmetry is one of the most important concepts of the science. In
physics and mathematics the symmetry allows one to simplify a problem, and
often to make it solvable. According to the Noether theorem symmetries are
responsible for conservation laws. Besides evident (explicit) spacetime
symmetries, responsible for conservation of energy, momentum, and angular
momentum of a system, there also exist what is called hidden symmetries, which
are connected with higher order in momentum integrals of motion. A remarkable
fact is that black holes in four and higher dimensions always possess a set
(`tower') of explicit and hidden symmetries which make the equations of motion
of particles and light completely integrable. The paper gives a general review
of the recently obtained results. The main focus is on understanding why at all
black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference
(June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan
Variational Approach to the Chiral Phase Transition in the Linear Sigma Model
The chiral phase transition at finite temperature is investigated in the
linear sigma model, which is regarded as a low energy effective theory of QCD
with three momentum cutoff, in the variational method with the Gaussian
approximation in the functional Schroedinger picture. It is shown that the
Goldstone theorem is retained and the meson pair excitations are automatically
included by taking into account the linear response to the external fields. It
is pointed out that the behavior of chiral phase transition depends on the
three-momentum cutoff, which leads to the careful treatment of the problem.Comment: 14 pages, 5 figures, using PTPTeX cl
Fluctuations and the Effective Moduli of an Isotropic, Random Aggregate of Identical, Frictionless Spheres
We consider a random aggregate of identical frictionless elastic spheres that
has first been subjected to an isotropic compression and then sheared. We
assume that the average strain provides a good description of how stress is
built up in the initial isotropic compression. However, when calculating the
increment in the displacement between a typical pair of contaction particles
due to the shearing, we employ force equilibrium for the particles of the pair,
assuming that the average strain provides a good approximation for their
interactions with their neighbors. The incorporation of these additional
degrees of freedom in the displacement of a typical pair relaxes the system,
leading to a decrease in the effective moduli of the aggregate. The
introduction of simple models for the statistics of the ordinary and
conditional averages contributes an additional decrease in moduli. The
resulting value of the shear modulus is in far better agreement with that
measured in numerical simulations
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