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Register a new userPoincare Series, 3D Gravity and CFT Spectroscopy
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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.
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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.
Dynamics at large redshift near the horizon of an extreme Kerr black hole are governed by an infinite-dimensional conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes. In this paper we compute and study the conformal transformation properties of the gravitational radiation emitted by an orbiting mass in the large-redshift near-horizon region.
Let $X$ be a compact Kahler manifold and $Lto X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences ${ |Lambda, krangle }_{k=1}^infty$, where $forall k$ $|Lambda, krangle$ is a holomorphic section of $L^{otimes k}$. The terms in each sequence concentrate on $Lambda$, and a sequence itself has a symbol which is a half-form, $sigma$, on $Lambda$. We prove estimates, as $ktoinfty$, of the norm squares $langle Lambda, k|Lambda, krangle$ in terms of $int_Lambda sigmaoverline{sigma}$. More generally, we show that if $Lambda_1$ and $Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $langleLambda_1, k|Lambda_2, krangle$ have an asymptotic expansion as $ktoinfty$, the leading coefficient being an integral over the intersection $Lambda_1capLambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincare series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.
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.
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