442 research outputs found
Consistent Pauli reduction of six-dimensional chiral gauged Einstein–Maxwell supergravity
Six-dimensional N=(1,0) Einstein-Maxwell gauged supergravity is known to
admit a (Minkowski)_4\times S^2 vacuum solution with four-dimensional N=1
supersymmetry. The massless sector comprises a supergravity multiplet, an SU(2)
Yang-Mills vector multiplet, and a scalar multiplet. In this paper it is shown
that, remarkably, the six-dimensional theory admits a fully consistent
dimensional reduction on the 2-sphere, implying that all solutions of the
four-dimensional N=1 supergravity can be lifted back to solutions in six
dimensions. This provides a striking realisation of the idea, first proposed by
Pauli, of obtaining a theory that includes Yang-Mills fields by dimensional
reduction on a coset space. We address the cosmological constant problem within
this model, and find that if the Kaluza-Klein mass scale is taken to be 10^{-3}
eV (as has recently been suggested) then four-dimensional gauge-coupling
constants for bulk fields must be of the order of 10^{-31}. We also suggest a
link between a modification of the model with 3-branes, and a five-dimensional
model based on an S^1/Z_2 orbifold.Comment: 20 pages, Latex. Discussion of compactification scale modified,
references adde
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
A String and M-theory Origin for the Salam-Sezgin Model
An M/string-theory origin for the six-dimensional Salam-Sezgin chiral gauged
supergravity is obtained, by embedding it as a consistent Pauli-type reduction
of type I or heterotic supergravity on the non-compact hyperboloid times . We can also obtain embeddings of larger, non-chiral,
gauged supergravities in six dimensions, whose consistent truncation yields the
Salam-Sezgin theory. The lift of the Salam-Sezgin (Minkowski)
ground state to ten dimensions is asymptotic at large distances to the
near-horizon geometry of the NS5-brane.Comment: Latex, 18 pages; minor correction
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
3-Branes and Uniqueness of the Salam-Sezgin Vacuum
We prove the uniqueness of the supersymmetric Salam-Sezgin
(Minkowski)_4\times S^2 ground state among all nonsingular solutions with a
four-dimensional Poincare, de Sitter or anti-de Sitter symmetry. We construct
the most general solutions with an axial symmetry in the two-dimensional
internal space, and show that included amongst these is a family that is
non-singular away from a conical defect at one pole of a distorted 2-sphere.
These solutions admit the interpretation of 3-branes with negative tension.Comment: Latex, 12 pages; typos corrected, discussion of brane tensions
amende
Flowing with Eight Supersymmetries in M-Theory and F-theory
We consider holographic RG flow solutions with eight supersymmetries and
study the geometry transverse to the brane. For both M2-branes and for
D3-branes in F-theory this leads to an eight-manifold with only a four-form
flux. In both settings there is a natural four-dimensional hyper-Kahler slice
that appears on the Coulomb branch. In the IIB theory this hyper-Kahler
manifold encodes the Seiberg-Witten coupling over the Coulomb branch of a U(1)
probe theory. We focus primarily upon a new flow solution in M-theory. This
solution is first obtained using gauged supergravity and then lifted to eleven
dimensions. In this new solution, the brane probes have an Eguchi-Hanson moduli
space with the M2-branes spread over the non-trivial 2-sphere. It is also shown
that the new solution is valid for a class of orbifold theories. We discuss how
the hyper-Kahler structure on the slice extends to some form of G-structure in
the eight-manifold, and describe how this can be computed.Comment: 29 pages, 1 figure, harvma
Supersymmetric M3-branes and G_2 Manifolds
We obtain a generalisation of the original complete Ricci-flat metric of G_2
holonomy on R^4\times S^3 to a family with a non-trivial parameter \lambda. For
generic \lambda the solution is singular, but it is regular when
\lambda={-1,0,+1}. The case \lambda=0 corresponds to the original G_2 metric,
and \lambda ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3
isometry group that acts on the S^3\times S^3 principal orbits. We then
construct explicit supersymmetric M3-brane solutions in D=11 supergravity,
where the transverse space is a deformation of this class of G_2 metrics. These
are solutions of a system of first-order differential equations coming from a
superpotential. We also find M3-branes in the deformed backgrounds of new
G_2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S.
Gubser and S. Gukov, and show that they also are supersymmetric.Comment: Latex, 29 pages. This corrects a previous version in which it was
claimed that the M3-brane solutions were pseudo-supersymmetric rather than
supersymmetri
Naturalness of CP violation in the standard model
We construct a natural measure on the space of Cabibbo-Kobayashi-Maskawa matrices in the standard model, assuming the fermion mass matrices are randomly selected from a distribution which incorporates the observed quark mass hierarchy. This measure allows us to assess the likelihood of Jarlskog’s CP violation parameter J taking its observed value J ≈ 3×10−5. We find that the observed value, while well below the mathematically allowed maximum, is in fact typical once the observed quark masses are assumed
New Complete Non-compact Spin(7) Manifolds
We construct new explicit metrics on complete non-compact Riemannian
8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is
topologically R^8 and another, which we denote by B_8, is the bundle of chiral
spinors over . Unlike the previously-known complete non-compact metric of
Spin(7) holonomy, which was also defined on the bundle of chiral spinors over
S^4, our new metrics are asymptotically locally conical (ALC): near infinity
they approach a circle bundle with fibres of constant length over a cone whose
base is the squashed Einstein metric on CP^3. We construct the
covariantly-constant spinor and calibrating 4-form. We also obtain an
L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of
opposite dualities) for the B_8 manifold. We use the metrics to construct new
supersymmetric brane solutions in M-theory and string theory. In particular, we
construct resolved fractional M2-branes involving the use of the L^2 harmonic
4-forms, and show that for each manifold there is a supersymmetric example. An
intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are
actually the same local solution, with the two different complete manifolds
corresponding to taking the radial coordinate to be either positive or
negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which
by contrast do not have special holonomy. In an appendix we construct the
general solution of our first-order equations for Spin(7) holonomy, and obtain
further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar
to B_8.Comment: Latex, 29 pages. Appendix obtaining general solution of first-order
equations and additional complete Spin(7) manifolds adde
Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
We consider non-relativistic electrons, each of the same charge to mass
ratio, moving in an external magnetic field with an interaction potential
depending only on the mutual separations, possibly confined by a harmonic
trapping potential. We show that the system admits a "relativity group" which
is a one-parameter family of deformations of the standard Galilei group to the
Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group.
This allows a group-theoretic interpretation of Kohn's theorem and related
results. Larmor's Theorem is used to show that the one-parameter family of
deformations are all isomorphic. We study the "Eisenhart" or "lightlike" lift
of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart
lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell
theory, which may also be regarded as a bi-invariant metric on the
Cangemi-Jackiw group.Comment: Typos corrected, references adde
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