321,424 research outputs found
Yang-Mills theory for semidirect products and its instantons
Yang-Mills theory with a symmetry algebra that is the semidirect product
defined by the coadjoint action of a Lie
algebra on its dual is studied. The gauge group
is the semidirect product , a
noncompact group given by the coadjoint action on of the Lie
group of . For simple, a
method to construct the self-antiself dual instantons of the theory and their
gauge non\-equivalent deformations is presented. Every instanton has an embedded instanton with the same instanton charge, in terms of which
the construction is realized. As an
example, and instanton charge one is
considered. The gauge group is in this case . Explicit
expressions for the selfdual connection, the zero modes and the metric and
complex structures of the moduli space are given.Comment: 21 pages; no figures; typos correcte
Seiberg--Witten maps for gauge invariance and deformations of gravity
A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity
is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge
symmetry are obtained for constant deformation parameters. This includes maps
for the vierbein, the spin connection and the Einstein--Hilbert Lagrangian. In
a second step the vierbein postulate is imposed in normal coordinates and the
deformation parameters are identified with the components
of a covariantly constant bivector. This procedure gives for the classical
action a power series in the bivector components which by construction is
diffeomorphism-invariant. Explicit contributions up to second order are
obtained. For completeness a cosmological constant term is included in the
analysis. Covariant constancy of , together with the
field equations, imply that, up to second order, only four-dimensional metrics
which are direct sums of two two-dimensional metrics are admissible, the
two-dimensional curvatures being expressed in terms of . These
four-dimensional metrics can be viewed as a family of deformed emergent
gravities.Comment: 1 encapsulated figur
Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes
The open string on the plane-wave limit of with constant
and dilaton background fields is canonically quantized. This entails
solving the classical equations of motion for the string, computing the
symplectic form, and defining from its inverse the canonical commutation
relations. Canonical quantization is proved to be perfectly suited for this
task, since the symplectic form is unambiguously defined and non-singular. The
string position and the string momentum operators are shown to satisfy
equal-time canonical commutation relations. Noticeably the string position
operators define non-commutative spaces for all values of the string
world-sheet parameter \sig, thus extending non-commutativity outside the
branes on which the string endpoints may be assumed to move. The Minkowski
spacetime limit is smooth and reproduces the results in the literature, in
particular non-commutativity gets confined to the endpoints.Comment: 31 pages, 12p
BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory
We prove that three-dimensional supersymmetric Yang-Mills-Chern-Simons
theory is finite to all loop orders. In general this leaves open the
possibility that different regularization methods lead to different finite
effective actions. We show that in this model dimensional regularization and
regularization by dimensional reduction yield the same effective action.
Consequently, the superfield approach preserves BRS invariance for this model.Comment: 27 pages, 2 figures, latex2e, uses epsfi
Higher covariant derivative regulators and non-multiplicative renormalization
The renormalization algorithm based on regularization methods with two
regulators is analyzed by means of explicit computations. We show in particular
that regularization by higher covariant derivative terms can be complemented
with dimensional regularization to obtain a consistent renormalized
4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid
regularization methods can be applied not only to finite theories, like \eg\
Chern-Simons, but also to divergent theories.Comment: 12 pages, phyzzx, no figure
Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD
We compute the beta function at one loop for Yang-Mills theory using as
regulator the combination of higher covariant derivatives and Pauli-Villars
determinants proposed by Faddeev and Slavnov. This regularization prescription
has the appealing feature that it is manifestly gauge invariant and essentially
four-dimensional. It happens however that the one-loop coefficient in the beta
function that it yields is not as it should be, but The
difference is due to unphysical logarithmic radiative corrections generated by
the Pauli-Villars determinants on which the regularization method is based.
This no-go result discards the prescription as a viable gauge invariant
regularization, thus solving a long-standing open question in the literature.
We also observe that the prescription can be modified so as to not generate
unphysical logarithmic corrections, but at the expense of losing manifest gauge
invariance.Comment: 43 pages, Latex file (uses the macro axodraw.sty, instructions of how
to get it and use it included), FTUAM 94/9, NIKHEF-H 94/2
Non-integrability of geodesic flow on certain algebraic surfaces
This paper addresses an open problem recently posed by V. Kozlov: a rigorous
proof of the non-integrability of the geodesic flow on the cubic surface . We prove this is the case using the Morales-Ramis theorem and Kovacic
algorithm. We also consider some consequences and extensions of this result.Comment: Accepted in Physics Letters
Smarandache's function applied to perfect numbers
Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n)! is divisible by n. In this article we are going to see that the value this function takes when n is a perfect number
On the Surface Tensions of Binary Mixtures
For binary mixtures with fixed concentrations of the species, various
relationships between the surface tensions and the concentrations are briefly
reviewed
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