Related papers: 3d Super Hyperbolic Geometry
We study properties of "hyperbolic directions" in groups acting cocompactly on properly convex domains in real projective space, from three different perspectives simultaneously: the (coarse) metric geometry of the Hilbert metric, the…
Representations of four dimensional superconformal groups are constructed as fields on many different superspaces, including super Minkowski space, chiral superspace, harmonic superspace and analytic superspace. Any unitary irreducible…
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of SL(2,$\mathbb{H}$). So after having related the 16-dim Dirac…
In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether…
We study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure coming from Poisson Lie theory. We construct completely…
A unitary transformation $\Ps [E]=\exp (i\O [E]/g) F[E]$ is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because $\o^a_i\equiv -\d\O…
Large-scale sublinearly Lipschitz maps have been introduced by Yves Cornulier in order to precisely state his theorems about asymptotic cones of Lie groups. In particular, Sublinearly biLipschitz Equivalences (SBE) are a weak variant of…
A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model,…
We determine the structure of the $*$-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra…
Let M be a complete hyperbolic 3-manifold of finite volume that admits a decomposition into right-angled ideal polyhedra. We show that M has a deformation retraction that is a virtually special square complex, in the sense of Haglund and…
The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite…
We characterize the Lie groups with finitely many connected components that are $O(u)$-bilipschitz equivalent (almost quasiisometric in the sense that the sublinear function $u$ replaces the additive bounds of quasiisometry) to the real…
We show that a spin-$5/2$ field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge "hypersymmetry" requires the presence of a finite number of additional fields,…
In this work we present novel and known three-dimensional hypergravity theories which are obtained by applying the powerful semigroup expansion method. We show that the expansion procedure considered here yields a consistent way of coupling…
The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…
Suppose $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1} is a Lie superalgebra of queer type or periplectic type over an algebraically closed field $\textbf{k}$ of characteristic $p>2$. In this article, we initiate preliminarily to…
We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…
The half-maximal supergravity theories in three dimensions, which have local $SO(8)\xz SO(n)$ and rigid SO(8,n) symmetries, are discussed in a superspace setting starting from the superconformal theory. The on-shell theory is obtained by…
We identify and study a class of hyperbolic 3-manifolds (which we call Macfarlane manifolds) whose quaternion algebras admit a geometric interpretation analogous to Hamilton's classical model for Euclidean rotations. We characterize these…
We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…