108 research outputs found
Tautological classes of definite 4-manifolds
We prove a diagonalisation theorem for the tautological, or generalised MillerāMoritaā Mumford, classes of compact, smooth, simply connected, definite 4āmanifolds. Our result can be thought of as a families version of Donaldsonās diagonalisation theorem. We prove our result using a families version of the BauerāFuruta cohomotopy refinement of SeibergāWitten theory. We use our main result to deduce various results concerning the tautological classes of such 4āmanifolds. In particular, we completely determine the tautological rings of CP2 and CP2 # CP2 . We also derive a series of linear relations in the tautological ring which are universal in the sense that they hold for all compact, smooth, simply connected definite 4āmanifolds.David Baragli
Leibniz algebroids, twistings and exceptional generalized geometry
We investigate a class of Leibniz algebroids which are invariant under
diffeomorphisms and symmetries involving collections of closed forms. Under
appropriate assumptions we arrive at a classification which in particular gives
a construction starting from graded Lie algebras. In this case the Leibniz
bracket is a derived bracket and there are higher derived brackets resulting in
an -structure. The algebroids can be twisted by a non-abelian
cohomology class and we prove that the twisting class is described by a
Maurer-Cartan equation. For compact manifolds we construct a Kuranishi moduli
space of this equation which is shown to be affine algebraic. We explain how
these results are related to exceptional generalized geometry.Comment: 58 page
Fine-grained parallelization of fitness functions in bioinformatics optimization problems: gene selection for cancer classification and biclustering of gene expression data
O-folds. Orientifolds and orbifolds in exceptional field theory
We describe conventional orientifold and orbifold quotients of string and M-theory in a unified approach based on exceptional field theory (ExFT). Using an extended spacetime, ExFT combines all the maximal ten and eleven dimensional supergravities into a single theory manifesting a global symmetry corresponding to the exceptional series of Lie groups. Here we will see how this extends to half-maximal theories by showing how a single \emph{generalised orbifold} (or O-fold), of ExFT gives rise to M-theory on an interval, type II with orientifold planes and the heterotic theories in an elegant fashion. We study in more detail such orbifold and orientifold actions preserving half-maximal supersymmetry, and show how the half-maximal structure of \EFT{} permits the inclusion of localised non-Abelian vector multiplets located at the orbifold fixed points. This allows us to reproduce for the example the expected modifications to the gauge transformations, Bianchi identities and actions of the theories obtained from the single ExFT starting point. We comment on the prospects of studying anomaly cancellation and more complicated, non-perturbative O-folds in the ExFT framework
Supersymmetric backgrounds, the Killing superalgebra, and generalised special holonomy
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