25 research outputs found
Topics on n-ary algebras
We describe the basic properties of two n-ary algebras, the Generalized Lie
Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and
comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and
Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology
relevant for the central extensions and infinitesimal deformations of FAs. It
is seen that semisimple FAs do not admit central extensions and, moreover, that
they are rigid. This extends the familiar Whitehead's lemma to all
FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is
no longer required to be fully skewsymmetric one is led to the n-Leibniz (or
Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz
algebras, those with an anticommutative n-bracket, we study the class of
n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first
n-1 entires of the n-Leibniz bracket.Comment: 11 page
Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion
We obtain the complete set of equations of motion for the interacting system
of supermembrane and dynamical D=4 N = 1 supergravity by varying its complete
superfield action and writing the resulting superfield equations in the special
gauge where the supermembrane Goldstone field is set to zero. We solve the
equations for auxiliary fields and discuss the effect of dynamical generation
of cosmological constant in the Einstein equation of interacting system and its
renormalization due to some regular contributions from supermembrane. These two
effects (discussed in late 70th and 80th, in the bosonic perspective and in the
supergravity literature) result in that, generically, the cosmological constant
has different values in the branches of the spacetime separated by the
supermembrane worldvolume.Comment: 23 pages, no figures. V2 two references added, 24 page
The historical fertility transition at the micro level: Southern Sweden 1815-1939
<b>Background</b>: We know a great deal about the historical fertility transition at the macro level. The dominating focus on the macro level in previous research on the fertility transition means, however, that to a large extent we lack knowledge about details of the decline and empirical tests of the leading explanatory frameworks. <b>Objective</b>: Our aim is to explore socioeconomic fertility differentials in an industrializing community, to gain insight about the details and discuss possible mechanisms. The study starts well before industrialization and finishes at the end of the transition. <b>Methods</b>: We use longitudinal individual-level data from the Scanian Economic-Demographic Database, which contains demographic as well as socioeconomic information, including occupation, landholding, and income. In the analysis we use hazard regressions with shared frailty at the family level. <b>Results</b>: The transition involved not only parity-specific stopping but also spacing. While the upper social strata had higher fertility prior to the transition, they started to control their fertility earlier, by the 1880s, and also more consistently. Farmers, the middle class, and skilled workers followed in the decades after, and unskilled workers with some additional delay. <b>Conclusions</b>: These findings are partly inconsistent with several of the major explanations in the literature, such as mortality decline, increased female labor force participation, and a quantity-quality trade-off, but consistent with an innovation process where new ideas and attitudes about family limitation spread from the elite to other social groups. <b>Comments</b>: Further studies are required to empirically test the innovation-diffusion theory
Unifying N=5 and N=6
We write the Lagrangian of the general N=5 three-dimensional superconformal
Chern-Simons theory, based on a basic Lie superalgebra, in terms of our
recently introduced N=5 three-algebras. These include N=6 and N=8
three-algebras as special cases. When we impose an antisymmetry condition on
the triple product, the supersymmetry automatically enhances, and the N=5
Lagrangian reduces to that of the well known N=6 theory, including the ABJM and
ABJ models.Comment: 19 pages. v2: Published version. Minor typos corrected, references
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On soft singularities at three loops and beyond
We report on further progress in understanding soft singularities of massless
gauge theory scattering amplitudes. Recently, a set of equations was derived
based on Sudakov factorization, constraining the soft anomalous dimension
matrix of multi-leg scattering amplitudes to any loop order, and relating it to
the cusp anomalous dimension. The minimal solution to these equations was shown
to be a sum over color dipoles. Here we explore potential contributions to the
soft anomalous dimension that go beyond the sum-over-dipoles formula. Such
contributions are constrained by factorization and invariance under rescaling
of parton momenta to be functions of conformally invariant cross ratios.
Therefore, they must correlate the color and kinematic degrees of freedom of at
least four hard partons, corresponding to gluon webs that connect four eikonal
lines, which first appear at three loops. We analyze potential contributions,
combining all available constraints, including Bose symmetry, the expected
degree of transcendentality, and the singularity structure in the limit where
two hard partons become collinear. We find that if the kinematic dependence is
solely through products of logarithms of cross ratios, then at three loops
there is a unique function that is consistent with all available constraints.
If polylogarithms are allowed to appear as well, then at least two additional
structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4;
added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11,
5.12 and 5.29); 38 pages, 3 figure
A Variational Deduction of Second Gradient Poroelasticity Part I: General Theory
Second gradient theories have to be used to capture how local micro
heterogeneities macroscopically affect the behavior of a continuum. In this
paper a configurational space for a solid matrix filled by an unknown amount of
fluid is introduced. The Euler-Lagrange equations valid for second gradient
poromechanics, generalizing those due to Biot, are deduced by means of a
Lagrangian variational formulation. Starting from a generalized Clausius-Duhem
inequality, valid in the framework of second gradient theories, the existence
of a macroscopic solid skeleton Lagrangian deformation energy, depending on the
solid strain and the Lagrangian fluid mass density as well as on their
Lagrangian gradients, is proven.Comment: 20 page