Asymptotic safety meets tensor field theory: Toward a new class of gravity-matter systems

Combining asymptotically safe quantum gravity with a tensor field theory, we exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a nonvanishing value of the scalar quartic coupling. We first present (further) evidence that in the asymptotic-safety paradigm, quantum fluctuations of gravity generically screen the quartic couplings in (multi)scalar models. For a tensor field theory in which the scalar field transforms under an internal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:msup><a:mo stretchy="false">)</a:mo><a:mn>3</a:mn></a:msup></a:math> symmetry, this has the effect of replacing asymptotic freedom, recently discovered at large <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>N</e:mi></e:math> on a fixed flat background, by an interacting fixed point in the presence of quantum gravity. The fixed point originates from the competition between the effects of the matter self-interactions which, contrary to the usual scalar models, are antiscreening, and the screening gravitational effects.