149 research outputs found
Field Redefinition Invariance in Quantum Field Theory
The issue of field redefinition invariance of path integrals in quantum field
theory is reexamined. A ``paradox'' is presented involving the reduction to an
effective quantum-mechanical theory of a -dimensional free scalar field
in a Minkowskian spacetime with compactified spatial coordinates. The
implementation of field redefinitions both before and after the reduction
suggests that operator-ordering issues in quantum field theory should not be
ignored.Comment: 7 page
Yang-Mills Solutions on Euclidean Schwarzschild Space
We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in
time-compactified Euclidean Schwarzschild space are actually time independent.
For these solutions, the Yang-Mills potential is constant along the time
direction (no barrier) and therefore, there is no tunneling. We also
demonstrate that the solutions found to date are three dimensional monopoles
and dyons. We conjecture that there are no time-dependent solutions in the
Euclidean Schwarzschild background.Comment: 12 pages, references added, version to appear in PR
Self-Duality in D <= 8-dimensional Euclidean Gravity
In the context of D-dimensional Euclidean gravity, we define the natural
generalisation to D-dimensions of the self-dual Yang-Mills equations, as
duality conditions on the curvature 2-form of a Riemannian manifold. Solutions
to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2
and Spin(7) holonomy. The equations in eight dimensions are a master set for
those in lower dimensions. By considering gauge fields propagating on these
self-dual manifolds and embedding the spin connection in the gauge connection,
solutions to the D-dimensional equations for self-dual Yang-Mills fields are
found. We show that the Yang-Mills action on such manifolds is topologically
bounded from below, with the bound saturated precisely when the Yang-Mills
field is self-dual. These results have a natural interpretation in
supersymmetric string theory.Comment: 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and
reference added, typos fixe
Gravitating Instantons In 3 Dimensions
We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theory
in three dimensional Euclidean space with cosmological constant. The classical
equations reduce to Bogomol'nyi type first order equations in curved space.
There are BPS type gauge theory instanton (monopole) solutions of finite action
in a gravitational instanton which itself has a finite action. We also discuss
gauge theory instantons in the vacuum (zero action) AdS space. In addition we
point out to some exact solutions which are singular.Comment: 17 pages, 4 figures, title has changed, gravitational instanton
actions are adde
A Comment on String Solitons
We derive an exact string-like soliton solution of D=10 heterotic string
theory. The solution possesses instanton structure in the
eight-dimensional space transverse to the worldsheet of the soliton.Comment: 4 page
Instanton-Meron Hybrid in the Background of Gravitational Instantons
When it comes to the topological aspects, gravity may have profound effects
even at the level of particle physics despite its negligibly small relative
strength well below the Planck scale. In spite of this intriguing possibility,
relatively little attempt has been made toward the exhibition of this
phenomenon in relevant physical systems. In the present work, perhaps the
simplest and the most straightforward new algorithm for generating solutions to
(anti) self-dual Yang-Mills (YM) equation in the typical gravitational
instanton backgrounds is proposed and then applied to find the solutions
practically in all the gravitational instantons known. Solutions thus obtained
turn out to be some kind of instanton-meron hybrids possessing mixed features
of both. Namely, they are rather exotic type of configurations obeying first
order (anti) self-dual YM equation which are everywhere non-singular and have
finite Euclidean YM actions on one hand while exhibiting meron-like large
distance behavior and carrying generally fractional topological charge values
on the other. Close inspection, however, reveals that the solutions are more
like instantons rather than merons in their generic natures.Comment: 33pages, Revtex, typos correcte
Yang-Mills Instantons Sitting on a Ricci-flat Worldspace of Double D4-brane
Thus far, there seem to be no complete criteria that can settle the issue as
to what the correct generalization of the Dirac-Born-Infeld (DBI) action,
describing the low-energy dynamics of the D-branes, to the non-abelian case
would be. According to recent suggestions, one might pass the issue of
worldvolume solitons from abelian to non-abelian setting by considering the
stack of multiple, coincident D-branes and use it as a guideline to construct
or censor the relevant non-abelian version of the DBI action. In this spirit,
here we are interested in the explicit construction of SU(2) Yang-Mills (YM)
instanton solutions in the background geometry of two coincident probe D4-brane
worldspaces particularly when the metric of target spacetime in which the probe
branes are embedded is given by the Ricci-flat, magnetic extremal 4-brane
solution in type IIA supergravity theory with its worldspace metric being given
by that of Taub-NUT and Eguchi-Hanson solutions, the two best-known
gravitational instantons. And then we demonstrate that with this YM instanton-
gravitational instanton configuration on the probe D4-brane worldvolume, the
energy of the probe branes attains its minimum value and hence enjoys stable
state provided one employs the Tseytlin's non-abelian DBI action for the
description of multiple probe D-branes. In this way, we support the arguments
in the literature in favor of Tseytlin's proposal for the non-abelian DBI
action.Comment: 39 pages, Revtex, some more comments adde
Translational invariance of the Einstein-Cartan action in any dimension
We demonstrate that from the first order formulation of the Einstein-Cartan
action it is possible to derive the basic differential identity that leads to
translational invariance of the action in the tangent space. The
transformations of fields is written explicitly for both the first and second
order formulations and the group properties of transformations are studied.
This, combined with the preliminary results from the Hamiltonian formulation
(arXiv:0907.1553 [gr-qc]), allows us to conclude that without any modification,
the Einstein-Cartan action in any dimension higher than two possesses not only
rotational invariance but also a form of \textit{translational invariance in
the tangent space}. We argue that \textit{not} only a complete Hamiltonian
analysis can unambiguously give an answer to the question of what a gauge
symmetry is, but also the pure Lagrangian methods allow us to find the same
gauge symmetry from the \textit{basic} differential identities.Comment: 25 pages, new Section on group properties of transformations is
added, references are added. This version will appear in General Relativity
and Gravitatio
An Efficient Representation of Euclidean Gravity I
We explore how the topology of spacetime fabric is encoded into the local
structure of Riemannian metrics using the gauge theory formulation of Euclidean
gravity. In part I, we provide a rigorous mathematical foundation to prove that
a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons
and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of
the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof
relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space
of two-forms splits canonically into the sum of three-dimensional vector spaces
of self-dual and anti-self-dual two-forms. Consolidating these two, it turns
out that the splitting of Spin(4) is deeply correlated with the decomposition
of two-forms on four-manifold which occupies a central position in the theory
of four-manifolds.Comment: 31 pages, 1 figur
Polynomial Hamiltonian form of General Relativity
Phase space of General Relativity is extended to a Poisson manifold by
inclusion of the determinant of the metric and conjugate momentum as additional
independent variables. As a result, the action and the constraints take a
polynomial form. New expression for the generating functional for the Green
functions is proposed. We show that the Dirac bracket defines degenerate
Poisson structure on a manifold, and a second class constraints are the Casimir
functions with respect to this structure. As an application of the new
variables, we consider the Friedmann universe.Comment: 33 pages, 1 figure, corrected reference
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