The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
arXiv:1202.1824 · doi:10.1103/PhysRevD.85.124030
Abstract
In this paper we consider the relation between the super-renormalizable theories of quantum gravity (SRQG) studied in [arXiv:1110.5249v2, arXiv:1202.0008] and an underlying non-commutativity of spacetime. For one particular super-renormalizable theory we show that at linear level (quadratic in the Lagrangian) the propagator of the theory is the same we obtain starting from a theory of gravity endowed with θ-Poincaré quantum groups of symmetry. Such a theory is over the so called θ-Minkowski non-commuative spacetime. We shed new light on this link and show that among the theories considered in [arXiv:1110.5249v2, arXiv:1202.0008], there exist only one non-local and Lorentz invariant super-renormalizable theory of quantum gravity that can be described in terms of a quantum group symmetry structure. We also emphasize contact with pre-existent works in the literature and discuss preservation of the equivalence principle in our framework.
10 pages
References in corpus (17)
- Towards singularity and ghost free theories of gravity
- A Gravity Theory on Noncommutative Spaces
- Noncommutative geometry inspired charged black holes
- Non-commutative geometry inspired higher-dimensional charged, black holes
- Charged rotating noncommutative black holes
- Black holes in an ultraviolet complete quantum gravity
- Noncommutative Inspired Black Holes in Extra Dimensions
- Statistics and UV-IR Mixing with Twisted Poincare Invariance
- Trace Anomaly in Quantum Spacetime Manifold
- Fock space, quantum fields and kappa-Poincaré symmetries
- From noncommutative kappa-Minkowski to Minkowski space-time
- The decay-time of non-commutative micro-black holes
- Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
- Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
- Un-graviton corrections to the Schwarzschild black hole
- Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle
- First results of the Noether theorem for Hopf-algebra spacetime symmetries
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