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We continue the study of the one-loop partition function of AdS3 gravity with focus on the square-integrability condition on the fluctuating fields. In a previous work we found that the Brown-Henneaux boundary conditions follow directly from the L2 condition. Here we rederive the partition function as a ratio of Laplacian determinants by performing a suitable decomposition of the metric fluctuations. We pay special attention to the asymptotics of the fields appearing in the partition function. We also show that in the usual computation using ghost fields for the de Donder gauge, such gauge condition is accessible precisely for square-integrable ghost fields. Finally, we compute the spectrum of the relevant Laplacians in thermal AdS3, in particular noticing that there are no isolated eigenvalues, only essential spectrum. This last result supports the analytic continuation approach of David, Gaberdiel and Gopakumar. The purely essential spectra found are consistent with the independent results of Lee and Delay of the essential spectrum of the TT rank-2 tensor Lichnerowickz Laplacian on asymptotically hyperbolic spaces. [ABSTRACT FROM AUTHOR]

We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window $$-3/4\le m_e^2\ell ^2<0$$ can be well defined within a one-parametric family of distinct boundary conditions ( $$-3/4$$ being the conformally coupled case), while for $$m_e^2\ell ^2\ge 0$$ the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for $$m_e^2\ell ^2<-1$$ , and also it is shown that in the range $$m_e^2\ell ^2 \in [-1,-3/4)$$ there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. [ABSTRACT FROM AUTHOR]

We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity. [ABSTRACT FROM AUTHOR]

We consider critical gravity in three dimensions; that is, the New Massive Gravity theory formulated about Anti-de Sitter (AdS) space with the specific value of the graviton mass for which it results dual to a two-dimensional conformal field theory with vanishing central charge. As it happens with Kerr black holes in four-dimensional critical gravity, in three-dimensional critical gravity the Bañados-Teitelboim-Zanelli black holes have vanishing mass and vanishing angular momentum. However, provided suitable asymptotic conditions are chosen, the theory may also admit solutions carrying non-vanishing charges. Here, we give simple examples of exact solutions that exhibit falling-off conditions that are even weaker than those of the so-called Log-gravity. For such solutions, we define the quasilocal stress-tensor and use it to compute conserved charges. Despite the drastic deformation of AdS $$_3$$ asymptotic, these solutions have non-zero mass and angular momentum, which we compute. [ABSTRACT FROM AUTHOR]

During the ’70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of λΦ 4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example — although does not capture all the difficulties in the constructive quantum field theory approach — allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach. [ABSTRACT FROM AUTHOR]

In the course of investigating regular subalgebras of E10(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E10(10) was uncovered (M. Henneaux et al., e-print hep-th/0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e., that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never ∞. We here go beyond subgroups of the Weyl group of E10(10) and classify all rank 10 Coxeter groups with these properties. We find 21 distinct Coxeter groups of which 7 were already described by M. Henneaux et al., (e-print hep-th/0606123). Moreover, we extend the classification to the rank 11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence index 4, of which at least 28 can be regularly embedded into E11(11). [ABSTRACT FROM AUTHOR]

Phase space path integral is worked out in a Riemannian geometry, by employing a prescription for the infinitesimal propagator that takes Riemann normal coordinates and momenta on an equal footing. The operator ordering induced by this prescription leads to the DeWitt curvature coupling in the Schrödinger equation. [ABSTRACT FROM AUTHOR]

A correction to the article "A Special Class of Rank 10 and 11 Coxeter Groups" is presented.

The partition function of three-dimensional quantum gravity has been argued to be one-loop exact. Here, we verify the vanishing of higher orders in perturbation theory by explicit computation in the second-order metric formulation at three loops. The number of one-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At two loops, we find that all such diagrams vanish separately after regularization. At three loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with nine diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.