Carroll Fermions

1. Well-written and easily understandable paper.
2. Technical details are also straight forward.

1. Slight lack of explanation at some points.
2. No practical reason for understanding Carroll fermions have been mentioned.

I could recommend the publication of the article “Carroll Fermions” by E.A.Bergshoeff et. Al. after some minor clarifications.

My doubts are the following:
1. Starting from eq.(2.1) and after rescaling the spacetime coordinates and Lorentz transformation parameters, the authors found eq.(2.5) and they claimed "only spatial rotations appear in the spin part of the transformation rule of the above Carroll fermion." But in the transformation eq.(2.1) there is also a factor $\Gamma_{AB}$ which I guess is the combination of gamma matrices. What is the reason behind not scaling this factor? Will it remain unaffected after taking Carroll limit? A similar doubt can be asked for the case of eq.(2.9).

2. In eq.(2.6) the authors have defined the Projection operator which satisfies the mentioned properties. As far as I know the projection operator is in general defined in terms of $\Gamma_*$ matrices instead of $\Gamma^0$. Is there any specific reason for choosing such definition?

3. The authors have written the electric Carroll Lagrangian in eq.(2.17) following the truncation eq.(2.16). For electric Carroll Lagrangian only $\psi_{+}$ and its Hermitian conjugate appear in the Lagrangian. It seems the degrees of freedom somehow got reduced compared to the relativistic fermions. Is it an artefact of the scaling procedure or the property of the electric Carroll theory? In the following section, the authors have mentioned the same action can be obtained by taking $\psi_- = 0$. Other than matching the actions what is the reason behind it?

4. Although the authors haven't mentioned anything about representations of $\Gamma$ matrices, I am curious about this. For the relativistic case, we know every representation of Cliff$(1,d)$ induces a representation of $so(1,d)$. Does in the Carroll case we get something like a contraction of $so(1,d)$?

5. As can be seen the mass term for electric (eq.(2.17)) and magnetic (eq.(2.23)) Carroll fermions are different. For the relativistic case, among the invariant bilinears $\bar{\psi}\psi$ and $\bar{\psi}\Gamma_*\psi$ are scalar and psedo-scalar respectively and accordingly one can get parity-even or parity-odd Lagrangian. Is it the same here?

1. Finally a systematic and clear analysis on the topic of Carroll fermions.
2. Well written paper, solid and elegant analysis.
3. The new results found in this paper will be useful for many upcoming applications.

1. While the results are expected to have many applications, no single application is given. Instead, the paper focusses on the construction of Lagrangians and couplings to gravity rather than on what to do with such models.

This paper shows significant progress on the construction of actions for Carroll fermions and their couplings to gravity. This topic is addressed before in the literature, but often in an unclear or un-elegant way, or in too specific cases. The results presented in this paper hold in arbitrary dimension, and with an elegant treatment of Dirac-gamma matrices in the Carroll limit. The techniques are solid, some of the authors have made important contributions in this field before and are experts. The presentation is very good and references are given to the literature in an appropriate way. I recommend publication.