1202.1824 (Stephon Alexander et al.)

The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity    [PDF]

Stephon Alexander, Antonino Marciano, Leonardo Modesto

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 {\theta}-Poincar\'e quantum groups of
symmetry. Such a theory is over the so called {\theta}-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.

View original: http://arxiv.org/abs/1202.1824