595 research outputs found
Beyond E11
We study the non-linear realisation of E11 originally proposed by West with
particular emphasis on the issue of linearised gauge invariance. Our analysis
shows even at low levels that the conjectured equations can only be invariant
under local gauge transformations if a certain section condition that has
appeared in a different context in the E11 literature is satisfied. This
section condition also generalises the one known from exceptional field theory.
Even with the section condition, the E11 duality equation for gravity is known
to miss the trace component of the spin connection. We propose an extended
scheme based on an infinite-dimensional Lie superalgebra, called the tensor
hierarchy algebra, that incorporates the section condition and resolves the
above issue. The tensor hierarchy algebra defines a generalised differential
complex, which provides a systematic description of gauge invariance and
Bianchi identities. It furthermore provides an E11 representation for the field
strengths, for which we define a twisted first order self-duality equation
underlying the dynamics.Comment: 97 pages. v2: Minor changes, references added. Published versio
An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies.
Relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death. We propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors. The baseline hazard was modelled until 10 years follow-up using parametric continuous functions. Six models including cubic regression splines were considered and the Akaike Information Criterion was used to select the final model. This approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information. Splines were also used to model simultaneously non-linear effects of continuous covariates and time-dependent hazard ratios. This led to a graphical representation of the hazard ratio that can be useful for clinical interpretation. Estimates of these models were obtained by likelihood maximization. We showed that these estimates could be also obtained using standard algorithms for Poisson regression
Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries
After adding 7 auxiliary scalars to the d=10 super-Yang-Mills action, 9 of
the 16 supersymmetries close off-shell. In this paper, these 9 supersymmetry
generators are related by dimensional reduction to scalar and vector
topological symmetry in =2 d=8 twisted super-Yang-Mills. Furthermore, a
gauge-invariant superspace action is constructed for d=10 super-Yang-Mills
where the superfields depend on 9 anticommuting theta variables.Comment: 15 page
String Theory, Unification and Quantum Gravity
An overview is given of the way in which the unification program of particle
physics has evolved into the proposal of superstring theory as a prime
candidate for unifying quantum gravity with the other forces and particles of
nature. A key concern with quantum gravity has been the problem of ultraviolet
divergences, which is naturally solved in string theory by replacing particles
with spatially extended states as the fundamental excitations. String theory
turns out, however, to contain many more extended-object states than just
strings. Combining all this into an integrated picture, called M-theory,
requires recognition of the r\^ole played by a web of nonperturbative duality
symmetries suggested by the nonlinear structures of the field-theoretic
supergravity limits of string theory.Comment: 29 pages, 13 figures, 3 tables; Lectures given at the 6th Aegean
Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos Island,
Greece, 12-17 September 201
Non-Abelian T-duality in Pre-Big-Bang Cosmology
We study the impact of non-Abelian T-duality transformations on a string
based cosmological model. The implementation of the pre-big-bang scenario is
investigated. We found a region of the dual phase where such a picture is
possible.Comment: 15 pages, LaTeX, 3 figure
On duality symmetries of supergravity invariants
The role of duality symmetries in the construction of counterterms for
maximal supergravity theories is discussed in a field-theoretic context from
different points of view. These are: dimensional reduction, the question of
whether appropriate superspace measures exist and information about non-linear
invariants that can be gleaned from linearised ones. The former allows us to
prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8
supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed
by the two other methods which can also be applied to D=4 theories with fewer
supersymmetries and allow us to prove that N=6 supergravity is finite at three
and four loops and that N=5 supergravity is three-loop finite.Comment: Clarification of arguments and their consistency with higher
dimensional divergences added, e.g. we prove the 5D 4L non-renormalisation
theorem. The 4L N=6 divergence is also ruled out. References adde
E{7(7)} Symmetry and Finiteness of N=8 Supergravity
We study N=8 supergravity deformed by the presence of the candidate
counterterms. We show that even though they are invariant under undeformed
E{7(7)}, all of the candidate counterterms violate the deformed E{7(7)} current
conservation. The same conclusion follows from the uniqueness of the Lorentz
and SU(8) covariant, E{7(7)} invariant unitarity constraint expressing the
56-dimensional E{7(7)} doublet via 28 independent vectors. Therefore E{7(7)}
duality predicts the all-loop UV finiteness of perturbative N=8 supergravity.Comment: 18 page
Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace
We formulate maximally supersymmetric Yang-Mills theory in five dimensions in
light-cone superspace. The light-cone Hamiltonian is of the quadratic form and
the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory
in four dimensions. We specifically study three-point counterterms and show how
these counterterms vanish on-shell. This study is a preliminary to set up the
technique in order to study possible four-point counterterms.Comment: 25 pages, typos corrected, references adde
String cosmology from Poisson-Lie T-dual sigma models on supermanifolds
We generalize the formulation of Poisson-Lie T-dual sigma models on manifolds
to supermanifolds. In this respect, we formulate 1+1 dimensional string
cosmological models on the Lie supergroup C^3 and its dual (A_1,1 +
2A)^0_(1,0,0), which are coupled to two fermionic fields. Then, we solve the
equations of motion of the models and show that there is a essential
singularity for the metric of the original model and its dual.Comment: 17 pages, Appendix and three references have adde
Duality covariant non-BPS first order systems
We study extremal black hole solutions to four dimensional N=2 supergravity
based on a cubic symmetric scalar manifold. Using the coset construction
available for these models, we define the first order flow equations implied by
the corresponding nilpotency conditions on the three-dimensional scalar momenta
for the composite non-BPS class of multi-centre black holes. As an application,
we directly solve these equations for the single-centre subclass, and write the
general solution in a manifestly duality covariant form. This includes all
single-centre under-rotating non-BPS solutions, as well as their
non-interacting multi-centre generalisations.Comment: 31 pages, v2: Discussion of the quadratic constraint clarified,
references added, typos corrected, published versio
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