Quantum Inflation of Classical Shapes

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization.Comment: 14 pages, Late

Can chaos be observed in quantum gravity?

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of nonintegrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.Comment: 6 pages + references -- matches published version (clarifications added for why GR with cosmologically interesting matter likely fails our notion of weak-integrability

Functional Renormalization of Noncommutative Scalar Field Theory

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the non-commutativity parameter, originally pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the $\phi^4$ coupling, recovering the result of \cite{disertori:2007}. Finally, we show how the FRGE can be easily used to compute the one loop beta-functions of the duality covariant model.Comment: 38 pages, no figures, LaTe

The Link between General Relativity and Shape Dynamics

We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity and Shape Dynamics, a theory with fixed foliation but spatial conformal invariance. This streamlines the rather complicated construction of this equivalence performed previously. We use this streamlined argument to extend the result to General Relativity with asymptotically flat boundary conditions. The improved understanding of linking theories naturally leads to the Lagrangian formulation of Shape Dynamics, which allows us to partially relate the degrees of freedom.Comment: 19 pages, LaTeX, no figure

Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections

Genome-Wide Association Study Identifies Two Novel Regions at 11p15.5-p13 and 1p31 with Major Impact on Acute-Phase Serum Amyloid A

Elevated levels of acute-phase serum amyloid A (A-SAA) cause amyloidosis and are a risk factor for atherosclerosis and its clinical complications, type 2 diabetes, as well as various malignancies. To investigate the genetic basis of A-SAA levels, we conducted the first genome-wide association study on baseline A-SAA concentrations in three population-based studies (KORA, TwinsUK, Sorbs) and one prospective case cohort study (LURIC), including a total of 4,212 participants of European descent, and identified two novel genetic susceptibility regions at 11p15.5-p13 and 1p31. The region at 11p15.5-p13 (rs4150642; p = 3.20×10−111) contains serum amyloid A1 (SAA1) and the adjacent general transcription factor 2 H1 (GTF2H1), Hermansky-Pudlak Syndrome 5 (HPS5), lactate dehydrogenase A (LDHA), and lactate dehydrogenase C (LDHC). This region explains 10.84% of the total variation of A-SAA levels in our data, which makes up 18.37% of the total estimated heritability. The second region encloses the leptin receptor (LEPR) gene at 1p31 (rs12753193; p = 1.22×10−11) and has been found to be associated with CRP and fibrinogen in previous studies. Our findings demonstrate a key role of the 11p15.5-p13 region in the regulation of baseline A-SAA levels and provide confirmative evidence of the importance of the 1p31 region for inflammatory processes and the close interplay between A-SAA, leptin, and other acute-phase proteins