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Register a new userColourful Poincare symmetry, gravity and particle actions
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We construct a generalisation of the three-dimensional Poincare algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincare gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincare symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.
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Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have positive spectrum. This allows us to efficiently extract the constraints on the CFT spectrum imposed by modular invariance, giving information on the spectrum that goes beyond the Cardy growth of the asymptotic density of states. Some of the candidate modular invariant partition functions we construct have gaps of size (c-1)/12, proving that gaps of this size and smaller are consistent with modular invariance. We also revisit the partition function of pure Einstein gravity in AdS3 obtained by summing over geometries, which has a spectrum with two unphysical features: it is continuous, and the density of states is not positive definite. We show that both of these can be resolved by adding corrections to the spectrum which are subleading in the semi-classical (large central charge) limit.
We explore Sakharovs seminal idea that gravitational dynamics is induced by the quantum corrections from the matter sector. This was the starting point of the view that gravity has an emergent origin, which soon gained impetus due to the advent of black hole thermodynamics. In the generalized framework of Riemann--Cartan spacetime with both curvature and torsion, the induced gravitational action is obtained for free nonminimally coupled scalar and Dirac fields. For a realistic matter content, the induced Newton constant is obtained to be of the magnitude of the ultraviolet cutoff, which implies that the cutoff is of the order of the Planck mass. Finally, we conjecture that the action for any gauge theory of gravity at low energies can be induced by Sakharovs mechanism. This is explicitly shown by obtaining the Poincare gauge theory of gravity.
We show that a recently proposed action for three-dimensional non-relativistic gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the co-adjoint Poincare algebra. We point out the similarity of our construction with the way that three-dimensional Galilei Gravity and Extended Bargmann Gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the Poincare algebra. We extend our results to the AdS case and we will see that there is a chiral decomposition both at the relativistic and non-relativistic level. We comment on possible further generalizations.
In this short note, based on the talk given at the 3rd Conference of the Polish Society on Relativity, I present the basic points of our recent paper Symmetries of quantum spacetime in three dimensions, stressing their physical meaning, and avoiding technical details.
2T-gravity in d+2 dimensions predicts 1T General Relativity (GR) in d dimensions, augmented with a local scale symmetry known as the Weyl symmetry in 1T field theory. The emerging GR comes with a number of constraints, particularly on scalar fields and their interactions in 1T field theory. These constraints, detailed in this paper, are footprints of 2T-gravity and could be a basis for testing 2T-physics. Some of the conceptually interesting consequences of the accidental Weyl symmetry include that the gravitational constant emerges from vacuum values of the dilaton and other Higgs-type scalars and that it changes after every cosmic phase transition (inflation, grand unification, electroweak phase transition, etc.). We show that this consequential Weyl symmetry in d dimensions originates from coordinate reparametrization, not from scale transformations, in the d+2 spacetime of 2T-gravity. To recognize this structure we develop in detail the geometrical structures, curvatures, symmetries, etc. of the d+2 spacetime which is restricted by a homothety condition derived from the action of 2T-gravity. Observers that live in d dimensions perceive GR and all degrees of freedom as shadows of their counterparts in d+2 dimensions. Kaluza-Klein (KK) type modes are removed by gauge symmetries and constraints that follow from the 2T-gravity action. However some analogs to KK modes, which we call prolongations of the shadows into the higher dimensions, remain but they are completely determined, up to gauge freedom, by the shadows in d dimensions.
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