22,237 research outputs found
Short Proofs for Cut-and-Paste Sorting of Permutations
We consider the problem of determining the maximum number of moves required
to sort a permutation of using cut-and-paste operations, in which a
segment is cut out and then pasted into the remaining string, possibly
reversed. We give short proofs that every permutation of can be
transformed to the identity in at most \flr{2n/3} such moves and that some
permutations require at least \flr{n/2} moves.Comment: 7 pages, 2 figure
On Holomorphic Effective Actions of Hypermultiplets Coupled to External Gauge Superfields
We study the structure of holomorphic effective action for hypermultiplet
models interacting with background super Yang-Mills fields. A general form of
holomorphic effective action is found for hypermultiplet belonging to arbitrary
representation of any semisimple compact Lie group spontaneously broken to its
maximal abelian subgroup. The applications of obtained results to
hypermultiplets in fundamental and adjoint representations of the SU(n), SO(n),
Sp(n) groups are considered.Comment: 8 pages, no figure
A class of Lorentzian Kac-Moody algebras
We consider a natural generalisation of the class of hyperbolic Kac-Moody
algebras. We describe in detail the conditions under which these algebras are
Lorentzian. We also construct their fundamental weights, and analyse whether
they possess a real principal so(1,2) subalgebra. Our class of algebras include
the Lorentzian Kac-Moody algebras that have recently been proposed as
symmetries of M-theory and the closed bosonic string.Comment: 40 pages TeX, 5 eps-figure
Duality Symmetries and G^{+++} Theories
We show that the non-linear realisations of all the very extended algebras
G^{+++}, except the B and C series which we do not consider, contain fields
corresponding to all possible duality symmetries of the on-shell degrees of
freedom of these theories. This result also holds for G_2^{+++} and we argue
that the non-linear realisation of this algebra accounts precisely for the form
fields present in the corresponding supersymmetric theory. We also find a
simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables
corrected, other minor changes, one appendix added, refs. added. Version
published in Class. Quant. Gra
Generalised geometry, eleven dimensions and E11
We construct the non-linear realisation of E11 and its first fundamental
representation in eleven dimensions at low levels. The fields depend on the
usual coordinates of space-time as well as two form and five form coordinates.
We derive the terms in the dynamics that contain the three form and six form
fields and show that when we restricted their field dependence to be only on
the usual space-time we recover the correct self-duality relation. Should this
result generalise to the gravity fields then the non-linear realisation is an
extension of the maximal supergravity theory, as previously conjectured. We
also comment on the connections between the different approaches to generalised
geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial
note added which gives the equation of motion relating the gravity field to
its dua
Generalised Space-time and Gauge Transformations
We consider the generalised space-time introduced by the author in 2003 in
the context of the non-linear realisation of the semi-direct product of E11 and
its first fundamental representation. For all the fields we propose gauge
transformations which are compatible with the underlying E11 structure. A
crucial role is played by the generalised vielbein that the generalised
space-time possess. We work out the explicit form of the gauge transformations,
at low levels, in four, five and eleven dimensions.Comment: 33 page
Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields
E11, generalised space-time and equations of motion in four dimensions
We construct the non-linear realisation of the semi-direct product of E11 and
its first fundamental representation at low levels in four dimensions. We
include the fields for gravity, the scalars and the gauge fields as well as the
duals of these fields. The generalised space-time, upon which the fields
depend, consists of the usual coordinates of four dimensional space-time and
Lorentz scalar coordinates which belong to the 56-dimensional representation of
E7. We demand that the equations of motion are first order in derivatives of
the generalised space-time and then show that they are essentially uniquely
determined by the properties of the E11 Kac-Moody algebra and its first
fundamental representation. The two lowest equations correctly describe the
equations of motion of the scalars and the gauge fields once one takes the
fields to depend only on the usual four dimensional space-time
The \chi Factor: Determining the Strength of Activity in Low Mass Dwarfs
We describe a new, distance-independent method for calculating the magnetic
activity strength in low mass dwarfs, L_{H\alpha}/L_{bol}. Using a
well-observed sample of nearby stars and cool standards spanning spectral type
M0.5 to L0, we compute ``\chi'', the ratio between the continuum flux near
H-alpha and the bolometric flux, f_{\lambda6560}/f_{bol}. This ratio may be
multiplied by the measured equivalent width of the H-alpha emission line to
yield L_{H\alpha}/L_{bol}. We provide \chi values for all objects in our
sample, as well as fits to \chi as a function of color and average values by
spectral type. This method was used by West et al.(2004) to examine trends in
magnetic activity strength in low mass stars.Comment: 11 pages, 5 figures. Accepted for publication in PAS
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