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Register a new userQuantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras
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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.
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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.
Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell systems. Various germane issues and all-loop renormalizability have been addressed. In the present work we make further progress by carrying out several additional tasks. Firstly, we present an alternative 4D covariant derivation of the physical state condition by examining gauge choice-independence of a scattering amplitude. To this end, a careful dichotomy between the ordinary, and large gauge symmetries is required and appropriate gauge-fixing of the ordinary symmetry must be performed. Secondly, vacuum energy is analyzed in a finite-temperature setup. A variant optimal perturbation theory is implemented to two-loop. The renormalized mass determined by the optimal perturbation theory turns out to be on the order of the temperature, allowing one to avoid the cosmological constant problem. The third task that we take up is examination of the possibility of asymptotic freedom in finite-temperature quantum electrodynamics. In spite of the debates in the literature, the idea remains reasonable.
We study the dS/CFT duality between minimal type-A higher-spin gravity and the free Sp(2N) vector model. We consider the bulk spacetime as elliptic de Sitter space dS_4/Z_2, in which antipodal points have been identified. We apply a technique from arXiv:1509.05890, which extracts the quantum-mechanical commutators (or Poisson brackets) of the linearized bulk theory in an *observable patch* of dS_4/Z_2 directly from the boundary 2-point function. Thus, we construct the Lorentzian commutators of the linearized bulk theory from the Euclidean CFT. In the present paper, we execute this technique for the entire higher-spin multiplet, using a higher-spin-covariant language, which provides a promising framework for the future inclusion of bulk interactions. Aside from its importance for dS/CFT, our construction of a Hamiltonian structure for a bulk causal region should be of interest within higher-spin theory itself. The price we pay is a partial symmetry breaking, from the full dS group (and its higher-spin extension) to the symmetry group of an observable patch. While the boundary field theory plays a role in our arguments, the results can be fully expressed within a boundary *particle mechanics*. Bulk fields arise from this boundary mechanics via a version of second quantization.
We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode which in perturbation theory has a ghostlike kinetic term, turns into a tachyon when nonlinear interaction is accounted for. The kinetic term and potential for this mode have opposite signs. Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.
Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a Weyl gauge transformation (of gauge fixing) while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number ($n_{df}$). The Weyl gauge field ($omega_mu$) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dynamic origin, as a transition from Weyl to Riemannian geometry. We show that a gauge fixing symmetry transformation of the original Weyl quadratic gravity action in its Weyl geometry formulation immediately gives the Einstein-Proca action for the Weyl gauge field and a positive cosmological constant, plus matter action (if present). As a result, the Planck scale is an {it emergent} scale, where Weyl gauge symmetry is spontaneously broken and Einstein action is the broken phase of Weyl action. This is in contrast to local scale invariant models (no gauging) where a negative kinetic term (ghost dilaton) remains present and $n_{df}$ is not conserved when this symmetry is broken. The mass of $omega_mu$, setting the non-metricity scale, can be much smaller than $M_text{Planck}$, for ultraweak values of the coupling ($q$). If matter is present, a positive contribution to the Planck scale from a scalar field ($phi_1$) vev induces a negative (mass)$^2$ term for $phi_1$ and spontaneous breaking of the symmetry under which it is charged. These results are immediate when using a Weyl geometry formulation of an action instead of its Riemannian picture. Briefly, Weyl gauge symmetry is physically relevant and its role in high scale physics should be reconsidered.
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