One-loop counterterms for dimensionally reduced quantum gravity

The technique of regularization by dimensional reduction is applied to source-free quantum gravity. The one-loop counterterms for the effective gravity-matter system are calculated in the background field formalism. The ersatz matter fields which arise in this regularization scheme are found to have no effect on the renormalizability of the theory.     

Convenient versus unique effective action formalism in 2d dilaton-Maxwell quantum gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effetive action are calculated in three different covariant gauges: (i) De Witt, (ii) Ω-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of theS-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.     

One-loop quantum gravity repulsion in the early Universe

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lema?tre-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.     

Chiral fermions in 2d quantum gravity

Two theories of chiral fermions coupled to different quantum gravities in two dimensions are studied. One employs Jackiw's ansatz for classical gravity by introducing an auxiliary scalar, the other is based on the induced quantum gravity of Polyakov, which has no classical analogue. By investigating a localized theory of the effective action we show that in both cases a limited number of fermions of either chirality may couple consistently. It is stressed that the Weyl variable has to be quantized properly, which is related to recent work done on non-critical strings.     

A new solution for dilaton-Maxwell gravity

An interesting static spherically symmetric solution corresponding to Einstein-Maxwell gravity coupled to a dilaton field with negative kinetic term has been obtained. This solution is characterized by the set of two arbitrary parameters, the physical mass ₀ and electric chargeQ. It has two horizons on which the metric, scalar curvature and both dilaton and electromagnetic fields are regular. Another feature of this solution is that the physical mass is bounded by the electric charge as ₀2¦Q¦ (unlike the Reisner-Nordström solution for which ₀>-¦Q¦). The structure of the scalar curvature has been analyzed.On leave from: Bogolyubov Institute for Theoretical Microphysics, Moscow State University, 119899 Moscow, Russia     

One-loop scalar field contributions to graviton-graviton scattering and helicity non-conservation in quantum gravity

We present and discuss the helicity amplitudes for graviton-graviton scattering via a loop of massless scalars. The amplitudes have the expected analytic structure but do not conserve helicity. We prove that as a consequence helicity is not conserved in pure quantum gravity either and the helicity flip amplitudes are given by two times the scalar loop contributions. Implications for the higher-loop renormalizability of quantum gravity are discussed.     

Local momentum-space representation of graviton propagators in an external gravitational field and one-loop counterterms in quantum gravity

Local momentum-space representation of graviton and ghost propagators in an arbitrary external gravitational field is constructed. It is shown that this representation allows to easily obtain one-loop counterterms in quantum gravity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 50–53, April, 1984.     

Observables in 3d spinfoam quantum gravity with fermions

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.     

New massive gravity and AdS(4) counterterms

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS(4)). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS(4) Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.     

2D quantum gravity from quantum entanglement

In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.     

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.     

One-loop photonic corrections to Bhabha scattering in d=4-2ε dimensions

The luminosity measurement at the projected International Linear e⁺e^- Collider ILC is planned to be performed with forward Bhabha scattering with an accuracy of the order of 10^-4. A theoretical prediction of the differential cross-section has to include one-loop weak corrections, with leading higher order terms, and the complete two-loop QED corrections. Here, we present the weak part and the virtual one-loop photonic corrections. For the photonic corrections, the expansions in ε=(4-d)/2 are derived with inclusion of the terms of order ε in order to match the two-loop accuracy. For the photonic box master integral in d dimensions we compare several different methods of evaluation.     

Scaling in quantum gravity

The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential falloff of the 2-point function with geodesic distance determines the fractal dimension d_H of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and d_H by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.