Quantization and fixed points of non-integrable Weyl theory

Carlo Pagani; Roberto Percacci

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Quantization and fixed points of non-integrable Weyl theory

Carlo Pagani, Roberto Percacci

High Energy Physics - Theory · Submitted 30 Dec 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We discuss the fixed points of these flows.

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We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations. We quantize the theory by suitably defining renormalization group flows that describe the integration of successive momentum shells, in such a way that Weyl--invariance is maintained in the flow. When the gauge fields are massless the theory has, in addition to Weyl invariance, an abelian gauge symmetry. According to the definition of the cutoff, the flow can break or preserve this extended symmetry. We discuss the fixed points of these flows.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations.	contribution 0.49	0.55	0.04	asserted 0.99
s1	We quantize the theory by suitably defining renormalization group flows that describe the integration of successive momentum shells, in such a way that Weyl--invariance is maintained in the flow.	method 0.98	0.93	0.09	asserted 1.00
s2	When the gauge fields are massless the theory has, in addition to Weyl invariance, an abelian gauge symmetry.	result 0.67	0.46	0.06	asserted 1.00
s3	According to the definition of the cutoff, the flow can break or preserve this extended symmetry.	result 0.33	0.31	0.09	hedged possibility 0.73
s4	We discuss the fixed points of these flows.	contribution 0.99	0.87	0.10	asserted 0.51

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Original abstract

We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations. We quantize the theory by suitably defining renormalization group flows that describe the integration of successive momentum shells, in such a way that Weyl--invariance is maintained in the flow. When the gauge fields are massless the theory has, in addition to Weyl invariance, an abelian gauge symmetry. According to the definition of the cutoff, the flow can break or preserve this extended symmetry. We discuss the fixed points of these flows.

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References

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Background independent exact renormalization group for conformally reduced gravity
hep-th 2015-02 conditional novelty 7.0 of 10

By combining the exact renormalization group flow with the modified split Ward identity in conformally reduced gravity, the authors derive a unique background-independent scale under which the flow equations become in...
A link that matters: Towards phenomenological tests of unimodular asymptotic safety
hep-th 2019-07 conditional novelty 6.0 of 10

Demanding that quantum gravity solve the Standard Model's Landau-pole problems restricts the viable parameter space of unimodular, Weyl-squared, and asymptotically safe gravity, with Weyl-squared results shown to be r...
En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
hep-th 2014-04 conditional novelty 6.0 of 10

Within a bi-metric Einstein-Hilbert truncation, a two-parameter family of asymptotically safe trajectories restores split-symmetry at zero scale, showing Background Independence and Asymptotic Safety are compatible.
Finite Conformal Quantum Gravity and Nonsingular Spacetimes
hep-th 2016-05 conditional novelty 5.0 of 10

Finite non-local quantum gravity is shown to be anomaly-free conformal gravity in a spontaneously broken phase, and conformal transformations map singular Schwarzschild, FRW, and BKL spacetimes to regular ones.
Spacetime completeness of non-singular black holes in conformal gravity
gr-qc 2016-11 conditional novelty 4.0 of 10

By rescaling the Schwarzschild and Kerr metrics with a conformal factor that diverges at the singularity, the authors obtain regular, geodesically complete black hole spacetimes in conformal gravity.

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7 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper

In this section we quantize the theory in exactly the same way carried out by Fradkin and Tsytlin in [ref] (see also [ref] ) for the local theory ([ref])[ In this subsection we define $g_μν ≡ϕ^2 ĝ_μν$, which slightly differs from ([ref]) because $[ϕ] = 0$ and in particular its exponent is here independent on the spacetime dimension $D$.

Finite Conformal Quantum Gravity and Nonsingular Spacetimes · Conformal quantum gravity in $D=4$ · 0.93

Cites it as background 2 papers

The way to preserve background Weyl invariance in the quantum theory has been discussed in [ref] .

Split Weyl transformations in quantum gravity · Weyl calculus · 0.96
Furthermore, many conceptual questions related to Asymptotic Safety have been addressed in [ref] .] Whether such a fixed point exists beyond finite-dimensional truncations and persists in a Lorentzian setting remains an open challenging problem [ref] , even though the first steps taken in [ref] and [ref] have yielded encouraging results in these directions already.

Scalar-Tensor theories within Asymptotic Safety · Introduction · 0.81

What it cites · 12 sentences without a confident label

Builds on 1 paper

In [ref] the result was extended to theories including matter, both minimally coupled and self-interacting.

The Renormalization Group and Weyl-invariance · Concluding remarks · 0.80

Uses the method or tool of 3 papers

Following [ref] , we parametrize the flow in terms of the dimensionless, constant, Weyl invariant parameter $u=k/χ$.

The Renormalization Group and Weyl-invariance · Introduction · 0.96
Such traces can be evaluated using the “universal RG machine” developed in [ref] .

Off-diagonal heat-kernel expansion and its application to fields with differential constraints · Derivation of the beta functions · 1.00
Here $Ψ=(h_μν,w_μ)$ is the multiplet formed by the fluctuation fields and $$ is a matrix in field space containing the couplings $g_i$, times a cutoff profile function $R_k$ which we choose to be $R_k(z)=(k^2-z)θ(k^2-z)$ [ref] .

Optimised Renormalisation Group Flows · The cutoff · 0.95

Compares with 5 papers

The calculation we have done here is very similar to the one in [ref] and finds a nonvanishing, positive coefficient.

QED coupled to QEG · Inside the massless subspace · 0.98
The RG flows studied in [ref] and [ref] did not preserve the special subspaces, in those cases.

Beta Function and Asymptotic Safety in Three-dimensional Higher Derivative Gravity · Introduction · 0.85
The RG flows studied in [ref] and [ref] did not preserve the special subspaces, in those cases.

One Loop Beta Functions in Topologically Massive Gravity · Introduction · 0.85

Cites as background 5 papers

This effect has been the subject of some interest in recent years [ref] .

Quantum gravity and charge renormalization · Inside the massless subspace · 0.94
This effect has been the subject of some interest in recent years [ref] .

Asymptotic freedom of Yang-Mills theory with gravity · Inside the massless subspace · 0.94
This effect has been the subject of some interest in recent years [ref] .

Gravitational Correction to Running of Gauge Couplings · Inside the massless subspace · 0.94

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