Lifshitz symmetry: Lie algebras, spacetimes and particles

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits ("particles") of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name "Lifshitz Lie algebras". We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes: (1) ($d+2$)-dimensional Lifshitz spacetimes which have one additional holographic direction; (2) ($d+1$)-dimensional Lifshitz--Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation; and (3) ($d+1$)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras. We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.Comment: 30 pages, 2 figures. (v2: added some references and acknowledgments.

From pp-Waves to Galilean Spacetimes

We exhibit all spatially isotropic homogeneous Galilean spacetimes of dimension $(n+1) \geq 4$, including the novel torsional ones, as null reductions of homogeneous pp-wave spacetimes. We also show that the pp-waves are sourced by pure radiation fields and analyse their global properties

Kinematical superspaces

We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and simplifies many of the calculations, we find a list of $43$ isomorphism classes of Lie superalgebras, some with parameters, whose (nontrivial) central extensions are also determined. We then classify their corresponding simply-connected homogeneous $(4|4)$-dimensional superspaces, resulting in a list of $27$ homogeneous superspaces, some with parameters, all of which are reductive. We determine the invariants of low rank and explore how these superspaces are related via geometric limits.Comment: 50 pages, 5 figures, 14 tables (v2: final version to appear in JHEP

Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature.Comment: 62 pages, 3 figures, 4 tables, v2: Matches published version, mistake corrected in Section 4.1.3., 10.2, 10.3, other minor improvements, added reference

Radiative decay of the lightest neutralino in an R-parity violating supersymmetric theory

In an R-parity violating supersymmetric scenario, the lightest neutralino $\tilde \chi^0_1$ is no longer a stable particle. We calculate the branching ratio for the decay mode $\tilde \chi^0_1 \longrightarrow \nu \gamma$ which occurs at the one-loop level. Taking into account bilinear as well as trilinear lepton number violating interactions as the sources of R-parity violation, we make a detailed scan of the parameter space, both with and without gaugino mass unification and including the constraints on the neutrino sector from the recent Superkamiokande results. This study enables one to suggest interesting experimental signals distinguishing between the two types of R-parity breaking, and also to ascertain whether such radiative decays can give rise to collider signals of the type $\gamma \gamma$ + $\not {\rm E}$ from pair-produced neutralinos.Comment: 25 pages, LaTex including postscript figures. Uses axodraw.sty. Minor typographic errors correcte

G-protein signaling: back to the future

Heterotrimeric G-proteins are intracellular partners of G-protein-coupled receptors (GPCRs). GPCRs act on inactive Gα·GDP/Gβγ heterotrimers to promote GDP release and GTP binding, resulting in liberation of Gα from Gβγ. Gα·GTP and Gβγ target effectors including adenylyl cyclases, phospholipases and ion channels. Signaling is terminated by intrinsic GTPase activity of Gα and heterotrimer reformation — a cycle accelerated by ‘regulators of G-protein signaling’ (RGS proteins). Recent studies have identified several unconventional G-protein signaling pathways that diverge from this standard model. Whereas phospholipase C (PLC) β is activated by Gαq and Gβγ, novel PLC isoforms are regulated by both heterotrimeric and Ras-superfamily G-proteins. An Arabidopsis protein has been discovered containing both GPCR and RGS domains within the same protein. Most surprisingly, a receptor-independent Gα nucleotide cycle that regulates cell division has been delineated in both Caenorhabditis elegans and Drosophila melanogaster. Here, we revisit classical heterotrimeric G-protein signaling and explore these new, non-canonical G-protein signaling pathways

Beyond Lorentzian symmetry

This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric properties required to define physical theories on the classified spacetime geometries. The work completed in substantiating this framework for kinematical, super-kinematical, and super-Bargmann symmetries constitutes the body of this thesis. To this end, the classification of kinematical Lie algebras in spatial dimension D = 3, as presented in [3,4], is reviewed; as is the classification of spatially-isotropic homogeneous spacetimes of [5]. The derivation of geometric properties such as the non-compactness of boosts, soldering forms and vielbeins, and the space of invariant affine connections is then presented. We move on to classify the N = 1 kinematical Lie superalgebras in three spatial dimensions, finding 43 isomorphism classes of Lie superalgebras. Once these algebras are determined, we classify the corresponding simply-connected homogeneous (4|4)-dimensional superspaces and show how the resulting 27 homogeneous superspaces may be related to one another via geometric limits. Finally, we turn our attention to generalised Bargmann superalgebras. In the present work, these will be the N = 1 and N = 2 super-extensions of the Bargmann and Newton-Hooke algebras, as well as the centrally-extended static kinematical Lie algebra, of which the former three all arise as deformations. Focussing solely on three spatial dimensions, we find 9 isomorphism classes in the N = 1 case, and we identify 22 branches of superalgebras in the N = 2 case

Lifshitz symmetry: Lie algebras, spacetimes and particles

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (``particles'') of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name "Lifshitz Lie algebras". We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes: 1. ($d+2$)-dimensional Lifshitz spacetimes which have one additional holographic direction; 2. ($d+1$)-dimensional Lifshitz—Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation; 3. and $(d+1)$-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras. We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits