The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are ``more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to T\overline{T}TT¯-deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS_33 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T}TT¯-deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining — in perturbation theory — a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of T\overline{T}TT¯-deformed theories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c})𝒪(1/c) in the 1/c1/c expansion.

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Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by GG and \LambdaΛ. As a consequence, correlation functions of the boundary stress tensor in AdS_33 are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS_33 gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a T\overline{T}TT¯-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order (GG being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

Chromosomal region 15q11-q13 has been implicated to harbor a susceptibility gene or genes underlying autism. Evidence has been derived from the existence of cytogenetic anomalies in this region associated with autism, and the report of linkage in a modest collection of multiplex families. Most recently, linkage disequilibrium with the marker GABRB3-155CA2 in the candidate locus GABRB3, located in this region, has been reported. We searched for linkage using eight microsatellite markers located in this region of chromosome 15 in 147 affected sib-pairs from 139 multiplex autism families. We also tested for linkage disequilibrium in the same set of families with the same markers. We found no evidence for excess allele sharing (linkage) for the markers in this region. Also, we found no evidence of linkage disequilibrium, including for the locus GABRB3-155CA2. Thus, it appears that the role of this region of chromosome 15 is minor, at best, in the majority of individuals with autism.

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