33,173 research outputs found
OM Theory and V-duality
We show that the (M5, M2, M2, MW) bound state solution of eleven
dimensional supergravity recently constructed in hep-th/0009147 is related to
the (M5, M2) bound state one by a finite Lorentz boost along a M5-brane
direction perpendicular to the M2-brane. Given the (M5, M2) bound state as a
defining system for OM theory and the above relation between this system and
the (M5, M2, M2', MW) bound state, we test the recently proposed V-duality
conjecture in OM theory. Insisting to have a decoupled OM theory, we find that
the allowed Lorentz boost has to be infinitesimally small, therefore resulting
in a family of OM theories related by Galilean boosts. We argue that such
related OM theories are equivalent to each other. In other words, V-duality
holds for OM theory as well. Upon compactification on either an electric or a
`magnetic' circle (plus T-dualities as well), the V-duality for OM theory gives
the known one for either noncommutative open string theories or noncommutative
Yang-Mills theories. This further implies that V-duality holds in general for
the little m-theory without gravity.Comment: 17 pages, typos corrected and references adde
Faster Existential FO Model Checking on Posets
We prove that the model checking problem for the existential fragment of
first-order (FO) logic on partially ordered sets is fixed-parameter tractable
(FPT) with respect to the formula and the width of a poset (the maximum size of
an antichain). While there is a long line of research into FO model checking on
graphs, the study of this problem on posets has been initiated just recently by
Bova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential
fragment of FO has an FPT algorithm for a poset of fixed width. We improve upon
their result in two ways: (1) the runtime of our algorithm is
O(f(|{\phi}|,w).n^2) on n-element posets of width w, compared to O(g(|{\phi}|).
n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow.
We complement this result by showing that, under a certain
complexity-theoretical assumption, the existential FO model checking problem
does not have a polynomial kernel.Comment: Paper as accepted to the LMCS journal. An extended abstract of an
earlier version of this paper has appeared at ISAAC'14. Main changes to the
previous version are improvements in the Multicoloured Clique part (Section
4
Cyclic cosmology from Lagrange-multiplier modified gravity
We investigate cyclic and singularity-free evolutions in a universe governed
by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as
well as in one. In the scalar case, cyclicity can be induced by a
suitably reconstructed simple potential, and the matter content of the universe
can be successfully incorporated. In the case of -gravity, cyclicity can
be induced by a suitable reconstructed second function of a very
simple form, however the matter evolution cannot be analytically handled.
Furthermore, we study the evolution of cosmological perturbations for the two
scenarios. For the scalar case the system possesses no wavelike modes due to a
dust-like sound speed, while for the case there exist an oscillation
mode of perturbations which indicates a dynamical degree of freedom. Both
scenarios allow for stable parameter spaces of cosmological perturbations
through the bouncing point.Comment: 8 pages, 3 figures, references added, accepted for publicatio
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