Search Results (4)

Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if $\mathcal{PT}$ symmetry is respected, and in that case, an equivalent Hermitian description exists via the so-called Dyson map. Generically, $\mathcal{PT}$-symmetric non-Hermitian theories can also feature phases where $\mathcal{PT}$ symmetry is broken and unitarity is lost. We review the construction of holographic duals to strongly coupled $\mathcal{PT}$-symmetric quantum field theories and the study of their phase diagram. We next focus on spacetime-dependent non-Hermitian couplings: non-Hermitian quenches and lattices. They violate the null energy condition in the gravity dual. The lattices realize phases supporting an imaginary current that breaks $\mathcal{PT}$ symmetry spontaneously. Remarkably, these non-Hermitian lattices flow to a $\mathcal{PT}$-symmetric fixed point in the IR. Full article

We review combinatorial quantum gravity, an approach that combines Einstein’s idea of dynamical geometry with Wheeler’s “it from bit” hypothesis in a model of dynamical graphs governed by the coarse Ollivier–Ricci curvature. This drives a continuous phase transition from a random to a geometric phase due to a condensation of loops on the graph. In the 2D case, the geometric phase describes negative-curvature surfaces with two inversely related scales: an ultraviolet (UV) Planck length and an infrared (IR) radius of curvature. Below the Planck scale, the random bit character survives; chunks of random bits of the Planck size describe matter particles of excitation energy given by their excess curvature. Between the Planck length and the curvature radius, the surface is smooth, with spectral and Hausdorff dimension 2. At scales larger than the curvature radius, particles see the surface as an effective Lorentzian de Sitter surface, the spectral dimension becomes 3, and the effective slow dynamics of particles, as seen by co-moving observers, emerges as quantum mechanics in Euclidean 3D space. Since the 3D distances are inherited from the underlying 2D de Sitter surface, we obtain curved trajectories around massive particles also in 3D, representing the large-scale gravity interactions. We thus propose that this 2D model describes a generic holographic screen relevant for real quantum gravity. Full article

A recent work proposed that the recent cosmic passage to a cosmic acceleration era is the result of the existence of small anti-gravity sources in each galaxy and clusters of galaxies. In particular, a Swiss-cheese cosmology model, which relativistically integrates the contribution of all these anti-gravity sources on a galactic scale has been constructed assuming the presence of an infrared fixed point for a scale dependent cosmological constant. The derived cosmological expansion provides an explanation for both the fine tuning and the coincidence problem. The present work relaxes the previous assumption on the running of the cosmological constant and allows for a generic scaling around the infrared fixed point. Our analysis reveals that, in order to produce a cosmic evolution consistent with the best $\Lambda$CDM model, the IR-running of the cosmological constant is consistent with the presence of an IR-fixed point. Full article

We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [Phys. Rev. D2020, 101, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of $\beta$-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of $\beta$-functions related to three couplings associated with $C^2$ (Weyl square), $\mathcal{G}$ (Gauss–Bonnet), and $R^2$ (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky $f\left(R\right)$ gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed. Full article