Related papers: Fractal Structure of Quantum Gravity in Two Dimens…
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a…
Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest…
In this paper, we prove the existence of two degrees of freedom that govern the movement of light in an expanding universe. The use of the fractal manifold model leads to reciprocal causality between variation of geometry and gravity, which…
We show that the fractonic dipole-conserving algebra can be obtained as an Aristotelian (and pseudo-Carrollian) contraction of the Poincar\'e algebra in one dimension higher. Such contraction allows to obtain fracton electrodynamics from a…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…
We measure the fractal structure of four dimensional simplicial quantum gravity by identifying so-called baby universes. This allows an easy determination of the critical exponent $\g$ connected to the entropy of four-dimensional manifolds.
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the…
We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the non-trivial fractal…
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
We investigate the interaction between matter and causal dynamical triangulations (CDT) in the context of two-dimensional quantum gravity. We focus on the Ising model coupled to CDT, contrasting this with Liouville gravity and the relation…
We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell closed string states. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number…