SciPost Submission Page
A non-lorentzian primer
by Eric Bergshoeff, José Figueroa-O'Farrill, Joaquim Gomis
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | José Figueroa-O'Farrill |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202212_00063v1 (pdf) |
| Date submitted: | Dec. 22, 2022, 7:04 p.m. |
| Submitted by: | José Figueroa-O'Farrill |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We review both the kinematics and dynamics of non-lorentzian theories and their associated geometries. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras. Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations. We explain the relation with the coadjoint orbit method. We continue discussing three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity. Introducing matter, we discuss electric and magnetic non-lorentzian field theories for three different spins: spin-0, spin-1/2 and spin-1, as limits of relativistic theories.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023-3-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00063v1, delivered 2023-03-08, doi: 10.21468/SciPost.Report.6867
Strengths
2). The review focusses on the most important examples and is not overly encyclopedic, while at the same time the relevant papers are cited where more examples (or special cases) can be found.
Weaknesses
Report
Requested changes
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item i). on page 2 is called non-relativistic holography, but the references are all in the context of the usual AdS/CFT correspondence so could the authors please clarify what is meant here.
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Refs [8,9] are independent of flat space holography. These are just the original Carroll papers. Should Carroll not be its own item in the list, surely it features in many more places than flat space holography.
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The authors refer to the Carroll limit as ultra-relativistic, but ultra-relativistic means v/c going to unity and so this viewpoint is really only correct if you view Carroll as originating from physics on a null hypersurface. If one does not take this higher-dimensional viewpoint it is better described as an ultra-local limit. It would be good if this is addressed in the text.
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Please clarify the notation used in (4.36) on the LHS of the first equality. I could not make sense of what is written there in an operational sense. The RHS of the second equality misses (\alpha).
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Below eq. (5.66) it is claimed that the equations displayed in (5.66) are related to the EOM of a magnetic Carroll scalar field theory (eq. (7.15)), but I do not agree with this. The EOM of (7.15) are not the equations in (5.66) so it was not clear to me what the authors meant by this comment. Please elaborate/clarify/modify.
Report #1 by Anonymous (Referee 1) on 2023-3-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00063v1, delivered 2023-03-07, doi: 10.21468/SciPost.Report.6861
Report
I think the article is excellent, the main highlight being the detailed exposition of the algebraic and geometric structures that underlie non-Lorentzian structures which replace the (pseudo) Riemannian metric structure of the relativistic spacetimes.
This is a rapidly growing field and hence any review can only do so much. If I were to be hyper-critical, I would mention that now there is a (partial?) understanding of fermions in the Carroll limit and this is a point that the authors don't address when considering the spin 1/2 case in their field theory section. But these nitpickings aside, I think this is an article that should be published as is in this journal.