Lie-algebraic classification of effective theories with enhanced soft limits

A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently by Cheung et al., and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO($n$) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.Comment: 1+48 pages; v2: minor changes and some references added, matches version published in JHE

Canonical D = 1 supergravity framework for FLRW cosmology

We construct an extension of standard flat FLRW cosmology with matter, possessing local D = 1, N = 1 proper-time supersymmetry. The fundamental equation for the resulting mini-superspace models of quantum universes is a Dirac-like analogue of the Friedmann and Wheeler-DeWitt equations. We provide solutions of this equation for specific matter configurations based on the supersymmetric O(3) and O(2, 1) sigma-models. It turns out that in the compact model the volume rate of growth of the universe is quantized and non-vanishing due to the zero-point energy of the scalar fields. In the non-compact model the spectrum of the growth rates is continuous but subject to an uncertainty relation involving the scale and the growth factor.Comment: 14 pages, no figure

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Tricuspid valvectomy is a rare surgical intervention, and knowledge regarding long-term outcome in children is lacking. We report a favourable outcome 11 years after tricuspid valvectomy in early infancy without subsequent surgery or other cardiac interventions. Specific criteria for timing of re-intervention are lacking. Application of adult tricuspid and pulmonary regurgitation recommendations is helpful but has limitations

From Symmetries to Scattering Amplitudes: A Lie-algebraic categorisation of symmetry-breaking patterns that create enhanced soft limits for NG bosons

The standard calculation of scattering amplitudes in quantum field theory is carried out using a perturbative expansion, that at successive orders contains an escalating number of terms to calculate. The amplitudes depend on an action, that specifies the properties and interactions of the particles involved in the scattering events. It is worthwhile to establish more direct relationships between the qualities of an action and its scattering amplitudes, not just to refine the formalism, but to simplify certain calculations. To that end, the long wavelength behaviour of the scattering amplitudes of Nambu-Goldstone bosons are investigated. NG bosons are massless scalar particles that exist due to, and whose interactions are principally determined by, the spontaneous breaking of symmetries; they make for good models to study the relations between symmetries and amplitudes. The subject here is specifically NG models with enhanced soft limits, meaning that, as the momentum of one of the particles entering a scattering event goes to zero, the amplitude must vanish as a higher power of that momentum. This thesis lays out the context and procedures that lead from symmetry breaking to effective actions and finally to the calculation of scattering amplitudes. Using this framework, the relation between Lie algebras and the enhanced soft limits was researched. In the case of a single physical NG boson, a full Lie algebraic categorisation of the models with enhanced scaling of the amplitudes in the soft limit was found: the only non-trivial models were the familiar DBI and galileon actions. For multiple physical NG bosons with enhanced soft limits a Lie algebra was discovered, which is purely determined by its internal, non-redundant symmetries, its affine representation and an invariant symmetric 2-tensor of said representation. From this algebra two infinite classes of models can be derived that are generalisations of the known DBI and galileon multi-flavour theories. The constraints on the amplitudes thus suffice to create categorisations of the Lie algebras. Due to the special properties of their soft limits, the resulting models may be interesting to high-energy physics and cosmology