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Register a new userDynamical dimensional reduction in toy models of 4D causal quantum gravity
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In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from numerical results on four-dimensional causal dynamical triangulations (CDT) [Ambjorn et al., Phys. Rev. Lett. 95 (2005) 171]. Since then little progress has been made in analytically understanding the numerical results coming from the CDT approach and showing that they remain valid when taking the continuum limit. Here we argue that the spectral dimension can be determined from a model with fewer degrees of freedom obtained from the CDTs by radial reduction. In the resulting toy model we can take the continuum limit analytically and obtain a scale dependent spectral dimension varying from four to two with scale and having functional behaviour exactly of the form which was conjectured on the basis of the numerical results.
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Recently a boundary energy-momentum tensor $T_{zz}$ has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an anomaly which is one-loop exact, $T_{zz}$ generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts $T_{zz}$.
Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an intrinsic length to objects in a QEG spacetime is also discussed.
It was shown in arXiv:1808.09428 that the modified 4d version of the KKLT model proposed in arXiv:1707.08678 is inconsistent for large values of the parameter $c$ advocated in arXiv:1707.08678, since there is a point in the moduli space where $|D_SW|^2$ vanishes. The authors responded with yet another modification of the 4d KKLT model arXiv:1809.06618. However, for large $c$, this model suffers from an even worse problem: not only is there a point in the moduli space where $|D_SW|^2$ vanishes, there is also a region in the moduli space where $|D_SW|^2$ is negative. Meanwhile for small $c$ these models have dS vacua. We construct improved models, which are fully consistent for all values of parameters, just as the original version of the KKLT model using a nilpotent superfield. These models have a family of dS vacua for a broad range of parameter values. Thus, the results of the analysis of all presently available consistent generalizations of the 4d KKLT model, in the domain of their validity, confirm the existence of dS vacua in the KKLT scenario.
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1|2) Dirac square root of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical BRST operator. The theory is a basic ingredient for building fundamental theories of physical observables.
We investigate the neutral AdS black-hole solution in the consistent $Drightarrow4$ Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B {bf 810}, 135843 (2020)] and construct the gravity duals of ($2+1$)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in ($2+1$)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency $omega_g/T_capprox 8$ in both ($2+1$)-dimensional s-wave and p-wave models.
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