16,306 research outputs found
Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
We study the action of picture-changing and spectral flow operators on a
ground ring of ghost number zero operators in the chiral BRST cohomology of the
closed N=2 string and describe an infinite set of symmetry charges acting on
physical states. The transformations of physical string states are compared
with symmetries of self-dual gravity which is the effective field theory of the
closed N=2 string. We derive all infinitesimal symmetries of the self-dual
gravity equations in 2+2 dimensional spacetime and introduce an infinite
hierarchy of commuting flows on the moduli space of self-dual metrics. The
dependence on moduli parameters can be recovered by solving the equations of
the SDG hierarchy associated with an infinite set of abelian symmetries
generated recursively from translations. These non-local abelian symmetries are
shown to coincide with the hidden abelian string symmetries responsible for the
vanishing of most scattering amplitudes. Therefore, N=2 string theory
"predicts" not only self-dual gravity but also the SDG hierarchy.Comment: 41 pages, no figure
Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
It is well known that there are no static non-Abelian monopole solutions in
pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions
exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times
S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions
of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely,
imposing SO(3)-invariance and some reality conditions, we consistently reduce
the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4
kink model whose static solutions give SU(N) monopole (-antimonopole)
configurations on the space R^{1,1}\times S^2 via the above-mentioned
correspondence. These solutions can also be considered as instanton
configurations of Yang-Mills theory in 2+1 dimensions. The kink model on
R^1\times S^1 admits also periodic sphaleron-type solutions describing chains
of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They
correspond to chains of n static monopole-antimonopole pairs on the space
R^1\times S^1\times S^2 which can also be interpreted as instanton
configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature
(thermal time circle). We also describe similar solutions in Euclidean SU(N)
gauge theory on S^1\times S^3 interpreted as chains of n
instanton-antiinstanton pairs.Comment: 16 pages; v2: subsection on topological charges added, title
expanded, some coefficients corrected, version to appear in PR
Shape of the inflaton potential and the efficiency of the universe heating
It is shown that the efficiency of the universe heating by an inflaton field
depends not only on the possible presence of parametric resonance in the
production of scalar particles but also strongly depends on the character of
the inflaton approach to its mechanical equilibrium point. In particular, when
the inflaton oscillations deviate from pure harmonic ones toward a succession
of step functions, the production probability rises by several orders of
magnitude. This in turn leads to a much higher temperature of the universe
after the inflaton decay, in comparison to the harmonic case. An example of the
inflaton potential is presented which creates a proper modification of the
evolution of the inflaton toward equilibrium and does not destroy the nice
features of inflation.Comment: 14 pages, 12 figures; final version published in EPJ
Solutions to Yang-Mills equations on four-dimensional de Sitter space
We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space
dS and construct a smooth and spatially homogeneous magnetic solution to
the Yang-Mills equations. Slicing dS as , via an
SU(2)-equivariant ansatz we reduce the Yang-Mills equations to ordinary matrix
differential equations and further to Newtonian dynamics in a double-well
potential. Its local maximum yields a Yang-Mills solution whose color-magnetic
field at time is given by , where for are the SU(2) generators and
is the de Sitter radius. At any moment, this spatially homogeneous
configuration has finite energy, but its action is also finite and of the value
in a spin- representation. Similarly, the
double-well bounce produces a family of homogeneous finite-action
electric-magnetic solutions with the same energy. There is a continuum of other
solutions whose energy and action extend down to zero.Comment: 1+7 pages; v2: introduction extended, gauge group representation
dependence added, minor clarifications, 3 more references; v3: title change,
published versio
Dressing Symmetries of Holomorphic BF Theories
We consider holomorphic BF theories, their solutions and symmetries. The
equivalence of Cech and Dolbeault descriptions of holomorphic bundles is used
to develop a method for calculating hidden (nonlocal) symmetries of holomorphic
BF theories. A special cohomological symmetry group and its action on the
solution space are described.Comment: 14 pages, LaTeX2
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