Limits of JT gravity

We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.

A free Lie algebra approach to curvature corrections to flat space-time

We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.

POLYVECTOR SUPER-POINCARÉ ALGEBRAS, M, F THEORY ALGEBRAS AND GENERALIZED SUPERSYMMETRY IN CLIFFORD-SPACES

Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic supersymmetric point-particle action in Clifford-space backgrounds. The relativistic supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector super-Poincaré and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-superspace realizations of generalized supersymmetries in Clifford spaces.

POINT PARTICLE–SYMMETRIC TENSORS INTERACTION AND GENERALIZED GAUGE PRINCIPLE

The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of external fields includes rank-0,1,2 symmetric tensors, so the whole system may be truncated to ordinary particle in Einstein–Maxwell backgrounds by switching off the higher-rank symmetric tensors. When otherwise all the higher rank tensors are switched on, the full gauge group provides a huge gauge symmetry acting on the whole infinite collection of symmetric tensors. We analyze this gauge symmetry and show that the symmetric tensors which couple to the point particle should not be interpreted as Fronsdal gauge fields, but rather as gauge fields of some conformal higher spin theories. It is shown that the Fronsdal fields system possesses twice as many symmetric tensor fields as is contained in the general background of the point particle. Besides, the particle action in general backgrounds is shown to reproduce De Wit–Freedman point particle–symmetric tensors first order interaction suggested many years ago, and extends their result to all orders in interaction, while the generalized equivalence principle completes the first order covariance transformations found in their paper, in all orders.

CONFORMAL INVARIANCE AND WAVE-PARTICLE DUALITY

We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configuration of dynamical variables. This leads to the geometrization of the quantum aspects of matter.