Renormalizability of nonlocal quantum gravity coupled to matter

We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle strongly constrained according to four consistency requirements: (i) all the classical solutions of Einstein's theory coupled to matter are also solutions of the nonlocal theory; (ii) such solutions have the same stability properties at the linear and nonlinear level; (iii) the tree-level scattering amplitudes are the same; (iv) macrocausality is not violated. At the quantum level, we prove that the theory is super-renormalizable in even dimensions and finite in odd dimensions. A simple extension of the model compatible with the above properties is finite also in even dimensions.

[1]  G. Calcagni,et al.  Quantum field theory with ghost pairs , 2022, Journal of High Energy Physics.

[2]  G. Calcagni,et al.  Tree-level scattering amplitudes in nonlocal field theories , 2021, Journal of High Energy Physics.

[3]  L. Modesto.  The Higgs mechanism in nonlocal field theory , 2021, Journal of High Energy Physics.

[4]  N. Ohta,et al.  Effective action from the functional renormalization group , 2020, The European Physical Journal C.

[5]  I. Shapiro,et al.  Gauge invariant renormalizability of quantum gravity , 2019, Physical Review D.

[6]  F. Briscese,et al.  Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories , 2018, Physical Review D.

[7]  Leslaw Rachwal,et al.  Nonlocal quantum gravity: A review , 2017 .

[8]  L. Modesto,et al.  Scattering amplitudes in super-renormalizable gravity , 2015, 1506.04589.

[9]  L. Modesto,et al.  Universally finite gravitational and gauge theories , 2015, 1503.00261.

[10]  L. Modesto,et al.  Super-renormalizable and finite gravitational theories , 2014, 1407.8036.

[11]  A. Mazumdar,et al.  Towards singularity- and ghost-free theories of gravity. , 2011, Physical review letters.

[12]  Leonardo Modesto,et al.  Super-renormalizable Quantum Gravity , 2011, 1107.2403.

[13]  G. Hooft.  A Class of Elementary Particle Models Without Any Adjustable Real Parameters , 2011, 1104.4543.

[14]  J. López,et al.  Some Remarks on High Derivative Quantum Gravity , 1996, hep-th/9610006.

[15]  E. Elizalde,et al.  A four-dimensional theory for quantum gravity with conformal and non-conformal explicit solutions , 1994, hep-th/9412061.

[16]  A. V. D. Ven.  Two-loop quantum gravity , 1992 .

[17]  Maeda.  Inflation as a transient attractor in R2 cosmology. , 1988, Physical review. D, Particles and fields.

[18]  N. Krasnikov.  Nonlocal gauge theories , 1987 .

[19]  Augusto Sagnotti,et al.  The ultraviolet behavior of Einstein gravity , 1986 .

[20]  A. Vilenkin,et al.  Classical and quantum cosmology of the Starobinsky inflationary model. , 1985, Physical review. D, Particles and fields.

[21]  A. Barvinsky,et al.  The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity , 1985 .

[22]  A. Starobinsky,et al.  A new type of isotropic cosmological models without singularity , 1980 .

[23]  M. Tonin,et al.  Quantum gravity with higher derivative terms , 1978 .

[24]  K. Stelle.  Renormalization of Higher Derivative Quantum Gravity , 1977 .

[25]  F. Englert,et al.  Conformal invariance in quantum gravity , 1976 .

[26]  S. Deser,et al.  One-loop divergences of quantized Einstein-Maxwell fields , 1974 .

[27]  Ermis Mitsou.  Non-local Gravity , 2016 .

[28]  E. Marcus.  Higher-derivative gauge and gravitational theories , 1998 .

[29]  G. Hooft,et al.  One loop divergencies in the theory of gravitation , 1974 .