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Renormalised spectral flows
by Jens Braun, Yong-rui Chen, Wei-jie Fu, Andreas Geißel, Jan Horak, Chuang Huang, Friederike Ihssen, Jan M. Pawlowski, Manuel Reichert, Fabian Rennecke, Yang-yang Tan, Sebastian Töpfel, Jonas Wessely, Nicolas Wink
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Submission summary
| Authors (as registered SciPost users): | Jens Braun · Wei-jie Fu · Andreas Geißel · Jan Horak · Chuang Huang · Jan M. Pawlowski · Manuel Reichert · Yang-yang Tan · Jonas Wessely · Nicolas Wink |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2206.10232v2 (pdf) |
| Date submitted: | 2022-08-26 10:14 |
| Submitted by: | Wink, Nicolas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows are manifestly finite in general non-perturbative truncation schemes also for regularisation schemes that do not implement an infrared suppression of the loops in the flow. Specifically, this formulation includes finite functional flows for the effective action with a spectral Callan-Symanzik cutoff, and therefore gives access to Lorentz invariant spectral flows. The functional setup is fully non-perturbative and allows for the spectral treatment of general theories. In particular, this includes theories that do not admit a perturbative renormalisation such as asymptotically safe theories. Finally, the application of the Lorentz invariant spectral functional renormalisation group is briefly discussed for theories ranging from real scalar and Yukawa theories to gauge theories and quantum gravity.
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Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2023-1-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2206.10232v2, delivered 2023-01-17, doi: 10.21468/SciPost.Report.6542
Report
This is a review paper introducing the functional renormalization group equipping with the spectral representation for propagator. In particular, the derivation and applications of the novel flow equation (38) are discussed. The paper is well-organised and especially the motivation is clearly written. I recommend this paper as an article in SciPost.
(i) Essential arguments, e.g. (17), (19) and (27), in Section IIIA rely on Ref. [30]. The authors should specify where the derivations of those equations are discussed in Ref. [30], like section ?? in [30] and equation ?? in [30].
(ii) Very minor things:
The last paragraph Section IIID, “one may has to” -> “one may have to”.
The abbreviation of the spacetime integral already is defined below Eq.(17), so that in Eqs.(63) and (A1) can be abbreviated.
What is the measure of integral in Eq.(A4)?