SciPost Submission Page
Intrinsically-defined higher-derivative Carrollian scalar field theories without Ostrogradsky instability
by Poula Tadros, Ivan Kolář
Submission summary
| Authors (as registered SciPost users): | Poula Tadros |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2409.03648v2 (pdf) |
| Date submitted: | 2024-09-13 10:41 |
| Submitted by: | Tadros, Poula |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants in the Lagrangian, thus, allowing interference solutions which are not allowed on a Lorentzian manifold. This demonstrates that the set of solutions to the Carrollian theories is much larger than that of their Lorentzian counterparts. We also show that Carrollian higher derivative theories are more resistant to Ostrogradsky's instabilities. These instabilities can be resolved by choosing the coupling constants appropriately in the Carrollian Lagrangian, something that was proven to be impossible in Lorentzian theories.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
The article under review considers Carrollian scalar fields and their novel properties, in particular their behaviour under Ostrogradsky instabilities that are known to exist in usual relativistic scalar field theories.
Carrollian symmetries are obtained by considering the vanishing speed of light limit of Poincare symmetries and of late have become of great interest in various diverse physical systems. The paper aims to address novel features of quantum field theories with underlying Carroll symmetry and this is a problem of relevance.
The authors wish to restrict their analysis to theories which are invariant under "Carrollian diffeomorphisms" and not necessarily under Carroll boosts. I find this to be the major problem in the paper. The most important distinguishing feature of Carrollian symmetry is the Carroll boost. This is what makes the system Carrollian. By choosing to neglect boosts, the authors, in my mind, give a completely incorrect idea of what should constitute a Carrollian theory.
The field theories that the authors consider are not Carrollian scalar theories because they are not invariant under Carroll boosts. In order for the subleading terms in the c-expansion to be Carroll invariant, one needs to add Lagrange multipliers to implement this Carroll boost invariance. Without them, these theories can never to claimed to be Carrollian scalar field theories.
I believe this very basic problem makes this paper unpublishable.
Recommendation
Reject
Strengths
1- The main strength of the paper is that it follows a timely and interesting subject, namely Carroll field theories, studied from an intrinsic Carrollian perspective
Weaknesses
1- The paper has elementary mistakes, see below my report
Report
The paper attempts to address interesting aspects of Carroll field theories.
However, it starts with a couple of elementary mistakes, some of which are more than just typos or oversights, so that my recommendation is to reject the paper.
Below is a selected list of these mistakes.
1- In the Jacobian (2.6) one of the j_a is incorrect and should be zero instead, since for Carroll diffeomoprhisms (2.5) x' depends only on x and not on t.
2- The wave operator defined between Eqs. (3.1) and (3.2) is incorrect; the derivatives should be covariant, not partial; alternatively, one could include a volume-form factor in parentheses to represent the Klein-Gordon operator using partial derivatives; either way, the current formula is wrong.
3- The claim at the start of section IV that h^{\mu\nu}\partial_\mu\phi\partial_\nu\phi is Carroll invariant is wrong; this expression is not Carroll boost invariant (and also not diff-invariant, see point 2- above) unless a further constraint is imposed. Indeed, as the authors can easily check using their Eq. (2.2), the quantity h^{\mu\nu} is not Carroll boost invariant.
These elementary, though relevant, mistakes do not inspire great confidence in the theorems presented in the paper. Therefore, the paper should be rejected.
Recommendation
Reject
Author: Poula Tadros on 2024-09-27 [id 4805]
(in reply to Report 1 on 2024-09-27)We would like to thank the referee for the time reviewing our paper.
Reply to points 1,3: The jacobian has a typo indeed, we will correct it in the resubmission. However, this part was not used in the rest of the paper since we construct the Lagrangian to be diffeomorphism invariant not Carroll boost invariant (as mentioned explicitly in the manscirpt) or Carroll diffeomorphism invariant (we will emphasise that also in the resubmission). All the formulae from (4.1) onwards only reuires diffeomorphism invariance not Carroll boost invariance, that also includes the beginning of section IV, the quantities are only constructed to be diffeomorphism invariant.
Reply to point 2: In this paper we consider flat manifolds (as indicated in the sentence before eq.(3.3)) so covariant derivatives are written as partial derivatives, then we use adapted coordinates later. However, we agree that it should be written as covariant derivatives in the occasion mentioned and we will do that in the resubmission.