657 research outputs found
A New Anomaly-Free Gauged Supergravity in Six Dimensions
We present a new anomaly-free gauged N=1 supergravity model in six
dimensions. The gauge group is E_7xG_2xU(1)_R, with all hyperinos transforming
in the product representation {56,14). The theory admits monopole
compactifications to R^4xS^2, leading to D=4 effective theories with broken
supersymmetry and massless fermions.Comment: 9 pages, RevTeX
Helfrich-Canham bending energy as a constrained non-linear sigma model
The Helfrich-Canham bending energy is identified with a non-linear sigma
model for a unit vector. The identification, however, is dependent on one
additional constraint: that the unit vector be constrained to lie orthogonal to
the surface. The presence of this constraint adds a source to the divergence of
the stress tensor for this vector so that it is not conserved. The stress
tensor which is conserved is identified and its conservation shown to reproduce
the correct shape equation.Comment: 5 page
Lipid membranes with an edge
Consider a lipid membrane with a free exposed edge. The energy describing
this membrane is quadratic in the extrinsic curvature of its geometry; that
describing the edge is proportional to its length. In this note we determine
the boundary conditions satisfied by the equilibria of the membrane on this
edge, exploiting variational principles. The derivation is free of any
assumptions on the symmetry of the membrane geometry. With respect to earlier
work for axially symmetric configurations, we discover the existence of an
additional boundary condition which is identically satisfied in that limit. By
considering the balance of the forces operating at the edge, we provide a
physical interpretation for the boundary conditions. We end with a discussion
of the effect of the addition of a Gaussian rigidity term for the membrane.Comment: 8 page
Variant N=(1,1) Supergravity and (Minkowski)_4 x S^2 Vacua
We construct the fermionic sector and supersymmetry transformation rules of a
variant N=(1,1) supergravity theory obtained by generalized Kaluza-Klein
reduction from seven dimensions. We show that this model admits both
(Minkowski)_4 x S^2 and (Minkowski)_3 x S^3 vacua. We perform a consistent
Kaluza-Klein reduction on S^2 and obtain D=4, N=2 supergravity coupled to a
vector multiplet, which can be consistently truncated to give rise to D=4, N=1
supergravity with a chiral multiplet.Comment: Latex, 17 pages. Version appearing in Classical and Quantum Gravit
Heisenberg-picture approach to the evolution of the scalar fields in an expanding universe
We present the Heisenberg-picture approach to the quantum evolution of the
scalar fields in an expanding FRW universe which incorporates relatively simply
the initial quantum conditions such as the vacuum state, the thermal
equilibrium state, and the coherent state. We calculate the Wightman function,
two-point function, and correlation function of a massive scalar field. We find
the quantum evolution of fluctuations of a self-interacting field
perturbatively and discuss the renormalization of field equations.Comment: 15 pages, RevTeX, no figure
Hamiltonian dynamics of extended objects
We consider a relativistic extended object described by a reparametrization
invariant local action that depends on the extrinsic curvature of the
worldvolume swept out by the object as it evolves. We provide a Hamiltonian
formulation of the dynamics of such higher derivative models which is motivated
by the ADM formulation of general relativity. The canonical momenta are
identified by looking at boundary behavior under small deformations of the
action; the relationship between the momentum conjugate to the embedding
functions and the conserved momentum density is established. The canonical
Hamiltonian is constructed explicitly; the constraints on the phase space, both
primary and secondary, are identified and the role they play in the theory
described. The multipliers implementing the primary constraints are identified
in terms of the ADM lapse and shift variables and Hamilton's equations shown to
be consistent with the Euler-Lagrange equations.Comment: 24 pages, late
Late time behaviour of the maximal slicing of the Schwarzschild black hole
A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be
evolved into a foliation of the -region of the spacetime by maximal
surfaces with the requirement that time runs equally fast at both spatial ends
of the manifold. This paper studies the behaviour of these slices in the limit
as proper time-at-infinity becomes arbitrarily large and gives an analytic
expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure
Instability of a membrane intersecting a black hole
The stability of a Nambu-Goto membrane at the equatorial plane of the
Reissner-Nordstr{\o}m-de Sitter spacetime is studied. The covariant
perturbation formalism is applied to study the behavior of the perturbation of
the membrane. The perturbation equation is solved numerically. It is shown that
a membrane intersecting a charged black hole, including extremely charged one,
is unstable and that the positive cosmological constant strengthens the
instability.Comment: 12 pages, 3 figures, to be published in Physical Review
Sharp bounds on the critical stability radius for relativistic charged spheres
In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a
lower bound on the radius of a charged sphere with mass M and charge Q<M is
addressed. Such a bound is referred to as the critical stability radius.
Equivalently, it can be formulated as the problem of finding an upper bound on
M for given radius and charge. This problem has resulted in a number of papers
in recent years but neither a transparent nor a general inequality similar to
the case without charge, i.e., M\leq 4R/9, has been found. In this paper we
derive the surprisingly transparent inequality
The
inequality is shown to hold for any solution which satisfies
where and are the radial- and tangential pressures respectively
and is the energy density. In addition we show that the inequality
is sharp, in particular we show that sharpness is attained by infinitely thin
shell solutions.Comment: 20 pages, 1 figur
Area-Constrained Planar Elastica
We determine the equilibria of a rigid loop in the plane, subject to the
constraints of fixed length and fixed enclosed area. Rigidity is characterized
by an energy functional quadratic in the curvature of the loop. We find that
the area constraint gives rise to equilibria with remarkable geometrical
properties: not only can the Euler-Lagrange equation be integrated to provide a
quadrature for the curvature but, in addition, the embedding itself can be
expressed as a local function of the curvature. The configuration space is
shown to be essentially one-dimensional, with surprisingly rich structure.
Distinct branches of integer-indexed equilibria exhibit self-intersections and
bifurcations -- a gallery of plots is provided to highlight these findings.
Perturbations connecting equilibria are shown to satisfy a first order ODE
which is readily solved. We also obtain analytical expressions for the energy
as a function of the area in some limiting regimes.Comment: 23 pages, several figures. Version 2: New title. Changes in the
introduction, addition of a new section with conclusions. Figure 14 corrected
and one reference added. Version to appear in PR
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