Hybrids in the genus Equisetum: an updated annotation

A list of authenticated hybrids in the genus Equisetum in Europe is given. This includes two hybrids in subgenus Hippochaete and six in subgenus Equisetum. Briefnotes on the morphology, ecology and distribution in Europe of each of the hybrids is given.Se presenta una lista de híbridos autentificados del género Equisetum en Europa, que incluye dos híbridos del subgénero Hippochaete y seis del subgénero Equisetum. Asimismo, se presentan unas breves notas sobre la morfología, ecología y distribución en Europa de cada uno de los híbridos citados

Resolutions of Cones over Einstein-Sasaki Spaces

Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous five-dimensional Einstein-Sasaki space Y^{2,1} was obtained. It was constructed by specialising the parameters in the BPS limit of recently-discovered Kerr-NUT-AdS metrics in higher dimensions. We study the occurrence of such non-singular resolutions of Calabi-Yau cones in a more general context. Although no further six-dimensional examples arise as resolutions of cones over the L^{pqr} Einstein-Sasaki spaces, we find general classes of non-singular cohomogeneity-2 resolutions of higher-dimensional Einstein-Sasaki spaces. The topologies of the resolved spaces are of the form of an R^2 bundle over a base manifold that is itself an $S^2$ bundle over an Einstein-Kahler manifold.Comment: Latex, 23 page

Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions

A generalisation of the four-dimensional Kerr-de Sitter metrics to include a NUT charge is well known, and is included within a class of metrics obtained by Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter metrics in arbitrary dimensions D \ge 6, which contain three non-trivial continuous parameters, namely the mass, the NUT charge, and a (single) angular momentum. We demonstrate the separability of the Hamilton-Jacobi and wave equations, we construct a closely-related rank-2 Staeckel-Killing tensor, and we show how the metrics can be written in a double Kerr-Schild form. Our results encompass the case of the Kerr-de Sitter metrics in arbitrary dimension, with all but one rotation parameter vanishing. Finally, we consider the real Euclidean-signature continuations of the metrics, and show how in a limit they give rise to certain recently-obtained complete non-singular compact Einstein manifolds.Comment: Author added, title changed, references added, focus of paper changed to Killing tensors and separability. Latex, 13 page

Weyl Group Invariance and p-brane Multiplets

In this paper, we study the actions of the Weyl groups of the U duality groups for type IIA string theory toroidally compactified to all dimensions $D\ge 3$. We show how these Weyl groups implement permutations of the field strengths, and we discuss the Weyl group multiplets of all supersymmetric $p$-brane solitons.Comment: 31 pages, Late

A G_2 Unification of the Deformed and Resolved Conifolds

We find general first-order equations for G_2 metrics of cohomogeneity one with S^3\times S^3 principal orbits. These reduce in two special cases to previously-known systems of first-order equations that describe regular asymptotically locally conical (ALC) metrics \bB_7 and \bD_7, which have weak-coupling limits that are S^1 times the deformed conifold and the resolved conifold respectively. Our more general first-order equations provide a supersymmetric unification of the two Calabi-Yau manifolds, since the metrics \bB_7 and \bD_7 arise as solutions of the {\it same} system of first-order equations, with different values of certain integration constants. Additionally, we find a new class of ALC G_2 solutions to these first-order equations, which we denote by \wtd\bC_7, whose topology is an \R^2 bundle over T^{1,1}. There are two non-trivial parameters characterising the homogeneous squashing of the T^{1,1} bolt. Like the previous examples of the \bB_7 and \bD_7 ALC metrics, here too there is a U(1) isometry for which the circle has everywhere finite and non-zero length. The weak-coupling limit of the \wtd\bC_7 metrics gives S^1 times a family of Calabi-Yau metrics on a complex line bundle over S^2\times S^2, with an adjustable parameter characterising the relative sizes of the two S^2 factors.Comment: Latex, 14 pages, Major simplification of first-order equations; references amende

p-brane Solitons in Maximal Supergravities

In this paper, we give a construction of $p$-brane solitons in all maximal supergravity theories in $4\le D \le 11$ dimensions that are obtainable from $D=11$ supergravity by dimensional reduction. We first obtain the full bosonic Lagrangians for all these theories in a formalism adapted to the $p$-brane soliton construction. The solutions that we consider involve one dilaton field and one antisymmetric tensor field strength, which are in general linear combinations of the basic fields of the supergravity theories. We also study the supersymmetry properties of the solutions by calculating the eigenvalues of the Bogomol'nyi matrices, which are derived from the commutators of the supercharges. We give an exhaustive list of the supersymmetric $p$-brane solutions using field strengths of all degrees $n=4,3,2,1$, and the non-supersymmetric solutions for $n=4,3,2$. As well as studying elementary and solitonic solutions, we also discuss dyonic solutions in $D=6$ and $D=4$. In particular, we find that the Bogomol'nyi matrices for the supersymmetric massless dyonic solutions have indefinite signature.Comment: 31 pages, Latex, no figure

Orientifolds and Slumps in G_2 and Spin(7) Metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which are complete on a complex line bundle over CP^3. The principal orbits are S^7, described as a triaxially squashed S^3 bundle over S^4. The behaviour in the S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S^4. We then consider new G_2 metrics which we denote by C_7, which are complete on an R^2 bundle over T^{1,1}, with principal orbits that are S^3\times S^3. We study the C_7 metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S^2 cycles, and both carry magnetic charge with respect to the R-R vector field. We also discuss some four-dimensional hyper-Kahler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(\infty) Toda equation, which can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction

Role of dynamical particle-vibration coupling in reconciliation of the d3/2d_{3/2} puzzle for spherical proton emitters

It has been observed that decay rate for proton emission from $d_{3/2}$ single particle state is systematically quenched compared with the prediction of a one dimensional potential model although the same model successfully accounts for measured decay rates from $s_{1/2}$ and $h_{11/2}$ states. We reconcile this discrepancy by solving coupled-channels equations, taking into account couplings between the proton motion and vibrational excitations of a daughter nucleus. We apply the formalism to proton emitting nuclei $^{160,161}$Re to show that there is a certain range of parameter set of the excitation energy and the dynamical deformation parameter for the quadrupole phonon excitation which reproduces simultaneously the experimental decay rates from the 2$d_{3/2}$, 3$s_{1/2}$ and 1$h_{11/2}$ states in these nuclei.Comment: RevTex, 12 pages, 4 eps figure

New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter

In this paper, which is an elaboration of our results in hep-th/0504225, we construct new Einstein-Sasaki spaces L^{p,q,r_1,...,r_{n-1}} in all odd dimensions D=2n+1\ge 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1)^{n+1} principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r_1,...,r_{n-1}), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds L^{p,q,r_1,...,r_{n-1}}. We also construct new complete and non-singular compact Einstein spaces \Lambda^{p,q,r_1,...,r_n} in D=2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken.Comment: latex, 26 page

Supersymmetric Non-singular Fractional D2-branes and NS-NS 2-branes

We obtain regular deformed D2-brane solutions with fractional D2-branes arising as wrapped D4-branes. The space transverse to the D2-brane is a complete Ricci-flat 7-manifold of G_2 holonomy, which is asymptotically conical with principal orbits that are topologically CP^3 or the flag manifold SU(3)/(U(1) x U(1)). We obtain the solution by first constructing an L^2 normalisable harmonic 3-form. We also review a previously-obtained regular deformed D2-brane whose transverse space is a different 7-manifold of G_2 holonomy, with principal orbits that are topologically S^3 x S^3. This describes D2-branes with fractional NS-NS 2-branes coming from the wrapping of 5-branes, which is supported by a non-normalisable harmonic 3-form on the 7-manifold. We prove that both types of solutions are supersymmetric, preserving 1/16 of the maximal supersymmetry and hence that they are dual to {\cal N}=1 three-dimensional gauge theories. In each case, the spectrum for minimally-coupled scalars is discrete, indicating confinement in the infrared region of the dual gauge theories. We examine resolutions of other branes, and obtain necessary conditions for their regularity. The resolution of many of these seems to lie beyond supergravity. In the process of studying these questions, we construct new explicit examples of complete Ricci-flat metrics.Comment: Latex, 30 page