Lagrangians for conformal gauge gravity and conformal simple supergravity

The connection, curvature, and Lagrangian for a conformal gauge gravity are obtained. A set of generators of the conformal simple supergroup is given, the commutation and anticommutation relations for the superalgebra are calculated, and a Lagrangian of the simple supergravity is established.     

Two-dimensional simplical quantum gravity

Quantum gravity in two dimensions is reviewed. Its formulation on simplicial lattices is described, with an action involving cosmological constant and higher derivative terms. Results are presented for the weak field approximation and for Monte Carlo calculations.     

Two-dimensional conformal quantum field theory

On leave of absence from the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria.     

On gauge independence in quantum gravity

We prove the gauge independence of the one-loop path integral for on-shell quantum gravity obtained in the framework of the modified geometric approach. We use a projector on pure gauge directions constructed via the quadratic form of the action. This enables us to formulate the proof entirely in terms of determinants of non-degenerate elliptic operators without reference to any renormalization procedure. The role of the rotation of the conformal factor in achieving gauge independence is discussed. Direct computations on CP² in a general three-parameter background gauge are presented. We comment on the gauge dependence of previous results by Ichinose.     

Ghost-free formulation of quantum gravity in the light-cone gauge

By choosing the light-cone gauge, we remove all redundant components of the metric tensor as well as all Faddeev-Popov ghosts from the Einstein Lagrangian, from which Feynman rules for two independent transverse components can be immediately formulated. The 2 + 2 decomposition of the metric tensor proves to be simpler than the usual canonical 1 + 3 decomposition, so that all spurious components can be explicitly eliminated from the spectrum. Because the Lagrangian is now only a function of independent components, it is possible to study the unresolved problem of the functional measure for quantum gravity. We are presently studying the measure problem.     

Asymptotic freedom in gauge theories and quantum gravity

Restrictions on the structure of a gauge theory which follow from the requirement of asymptotic freedom with respect to all coupling constants are studied. One-loop counterterms for renormalizable gravity with matter are computed. It is shown that for the group O(N), taking into account the contribution of quantum R²-gravity allows one to construct new, asymptotically free gauge theories with a reduced number of spinor multiplets. The results are compared with those obtained earlier for conformal gravity with matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–41, January, 1990.The authors thank A. O. Barvinskii, I. L. Bukhbinder, and E. S. Fradkin for the discussions.     

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F⁺ (H_graviton) where the one-particle Hilbert space H_graviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space H_graviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.     

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of U(1)$U\left(1\right)$ lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.     

Two-dimensional quantum gravity and current algebra on a torus

The euclidean generating functional of the correlation functions of the energy-momentum tensor in conformal field theory on a torus is derived. The quantization of the effective action for induced two-dimensional gravity on the torus is still related to the SU(2)×SU(2) current algebra.     

Conformal off-mass-shell extension and elimination of conformal anomalies in quantum gravity

Radiative corrections in the Einstein quantum gravity are made manifestly conformally invariant without changing the S matrix. The conformally invariant form of the classical gravitational action is restored. It is shown, that conformal anomalies, discovered in gravitating systems, do not affect the S matrix. Off the mass shell these anomalies are eliminated by the appropriate choice of a regularization.     

Curved space-time formulation of the conformal sector for 4D quantum gravity

Developing the approach by Antoniadis and mottola to 4D quantum gravity, we investigate the dynamics of the conformal factor of 4D induced gravity in arbitrary curved background. The one-loop -functions are calculated in infrared stable fixed point where the effective scalar theory is multiplicatively renormalized.     

Instantons in conformal gravity

We study extrema of the general conformally invariant action:

$\text{S}{}_{\mathrm{c}}\text{= ∫}\text{1}\text{α}{}^2\text{C}{}^{\mathrm{abcd}}\text{C}{}_{\mathrm{abcd}}\text{+γR}{}^{\mathrm{abcd}}{}^1\text{R}{}_{\mathrm{abcd}}{}^1\text{+iθR}{}^{\mathrm{abcd}}\text{1R}{}_{\mathrm{abcd}}$

.We find the first examples in four dimensions of asymptotically euclidean gravitational instantons. These have arbitrary Euler number and Hirzebruch signature. Some of these instantons represent tunneling between zero-curvature vacua that are not related by small gauge transformations. Others represent tunneling between flat space and topologically non-trivial zero-energy initial data. A general formula for the one-loop determinant is derived in terms of the renormalization group invariant masses, the volume of space-time, the Euler number and the Hirzebruch signature.     

Metric-torsional conformal gravity

When in general geometric backgrounds the metric is accompanied by torsion, the metric conformal properties should correspondingly be followed by analogous torsional conformal properties; however a combined metric torsional conformal structure has never been found which provides a curvature that is both containing metric-torsional degree of freedom and conformally invariant: in this Letter we construct such a metric-torsional conformal curvature. We proceed by building the most general action, then deriving the most general system of field equations; we check their consistency by showing that both conservation laws and trace condition are verified. Final considerations and comments are outlined.