4,082 research outputs found
Status of background-independent coarse-graining in tensor models for quantum gravity
A background-independent route towards a universal continuum limit in
discrete models of quantum gravity proceeds through a background-independent
form of coarse graining. This review provides a pedagogical introduction to the
conceptual ideas underlying the use of the number of degrees of freedom as a
scale for a Renormalization Group flow. We focus on tensor models, for which we
explain how the tensor size serves as the scale for a background-independent
coarse-graining flow. This flow provides a new probe of a universal continuum
limit in tensor models. We review the development and setup of this tool and
summarize results in the 2- and 3-dimensional case. Moreover, we provide a
step-by-step guide to the practical implementation of these ideas and tools by
deriving the flow of couplings in a rank-4-tensor model. We discuss the
phenomenon of dimensional reduction in these models and find tentative first
hints for an interacting fixed point with potential relevance for the continuum
limit in four-dimensional quantum gravity.Comment: 28 pages, Review prepared for the special issue "Progress in Group
Field Theory and Related Quantum Gravity Formalisms" in "Universe
Evidence for a novel shift-symmetric universality class from the functional renormalization group
Wetterich's equation provides a powerful tool for investigating the existence
and universal properties of renormalization group fixed points exhibiting
quantum scale invariance. Motivated by recent works on asymptotically safe
scalar-tensor theories, we develop a novel approximation scheme which projects
the functional renormalization group equation onto functions of the kinetic
term. Applying this projection to scalars and gauge fields, our analysis
identifies a new universality class with a very special spectrum of stability
coefficients. The implications of our findings in the context of asymptotically
safe gravity-matter systems are discussed.Comment: 10 pages, 3 figure
The fate of chiral symmetry in Riemann-Cartan geometry
We study the mechanism of chiral symmetry breaking for fermionic systems in a
gravitational background with curvature and torsion. The analysis is based on a
scale-dependent effective potential derived from a bosonized version of the
Nambu-Jona-Lasino model in a Riemann-Cartan background. We have investigated
the fate of chiral symmetry in two different regimes. First, to gain some
intuition on the combined effect of curvature and torsion, we investigate the
regime of weak curvature and torsion. However, this regime does not access the
deep infrared limit, which is essential to answer questions related to the
mechanism of gravitational catalysis in fermionic systems. Second, we look at
the regime of vanishing curvature and homogeneous torsion. In this case,
although we cannot probe the combined effects of curvature and torsion, we can
access the deep infrared contributions of the background torsion to the
mechanism of chiral symmetry breaking. Our main finding is that, in the
scenario where only torsion is present, there is no indication of a mechanism
of gravitational catalysis.Comment: 18 pages, 2 figure
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