Supersymmetric HS Yang-Mills-like Models

Round 1

Reviewer 1 Report

This paper performs the supersymmetrization of higher spin Yang-Mill models via the supefield formalism. It is an interesting piece of work and the results are clearly illustrated and derived. I therefore recommend it for publication on Universe.

Author Response

We thank the referee for the comment

Reviewer 2 Report

This interesting article constructs the action for supersymmetric self-interacting higher spin (HS) theories and explores the symmetries of the resulting models. Incorporation of interactions into the HS theories is a notoriously difficult problem, and the authors have made an impressive progress towards solving it. This paper will be interesting to a wide audience of researchers, and I recommend this article for publication in Universe once the following two issues are addressed.

1. The analysis presented in the paper appears to be purely classical. I would recommend adding some comments about quantizing the system (although solving the problem in full detail would constitute separate publications, and I don't advocate such major revision). In particular, quantization of the ordinary Yang-Mills theory becomes consistent only once ghost fields are introduced, so it would be beneficial to have some statements about the possibility for introducing such ghosts for HS fields. The sentence in lines 39-40 is not sufficient to address the problem of quantization.

2. Given the long history of attempts to construct actions for HS spin fields and to quantize them, the list of four references, one of which is a textbook, is not appropriate. I would recommend presenting a better overview of the existing literature and comparing it with the approach presented in this article. 

I recommend this article for publication after the proposed changes are implemented. 

Author Response

We thank the referee for her/his report. We agree with her/his criticisms and in the revised version we try to comply with them. Although a satisfactory answer to point 1) would require further research work and another paper (as the referee recognizes), we have added a paragraph at the end of section 3 to provide some insight in the possibility of a BRST quantization. As we explain it is certainly feasible along the lines of the paper:
L. Bonora, "BRST and supermanifolds", Nucl. Phys. B (2016), http://dx.doi.org/10.1016/j.nuclphysb.2016.03.001
For the referee convenience we attach to this reply a pdf containing the relevant part of that paper.

As for point 2) we have added a part of the vast bibliography on HS that we consider significant for our paper. Our changes of the manuscript are in blue.

Author Response File: Author Response.pdf

Reviewer 3 Report

please see attachment

Comments for author File: Comments.pdf

Author Response

We thank the referee for the report, although we have not been pleased by its negative attitude. We think this is due to a miscomprehension of our paper. The referee's criticisms focus on the very first part of it. Now, the first part is a summary of a previous paper. Probably we have not been clear enough, also because, in order to keep the summary to a reasonable extent, we have skept all the discussion about local Lorentz invariance, with the understanding that an analogous discussion for the supersymmetric case can be found in section 4. Anyhow, here we are to try to spell out the referee's doubts.

Let us start by saying that our scheme is teleparallelism. Now, this term may have two meanings: on the one hand it refers to a geometric scheme, on the other hand to a specific gravity action. Our use of the word refers only the scheme (no relation with the teleparallel action). The teleparallel scheme consists of the separation between the inertial and the dynamical degrees of freedom. For instance the vierbein splits into two parts, an inertial part, say e , which is made of purely local Lorentz dofs, and the dymamical part, say E-e. These two parts keep separate throughout the paper. Contrary to the usual approach in Riemannian geometry, they do not form a unique field. In fact we never use the complete frame E in formulating the theory. An analogous relation holds for the connection: there is an inertial connection with vanishing curvature, while the dynamical part is contained in a covariant tensor, the torsion (or contorsion).
In our paper what we call frame master field h_a contains the fluctuating dynamical part of the vierbein, it DOES NOT contain the inertial part. In the initial formulation of HS-YM, the local Lorentz symmetry is fixed, so the inertial part e at the beginning shows up as a Kronecker delta that collapses the tangent spacetime to the ('curved', but we should rather call it 'contorted') spacetime. Later on, after Lorentz covariance is implemented, the inertial part e of the vierbein plays a different role: it shows up in the determinant which guarantees covariance of the action integral and, for instance, in A_a -> e_a^\mu A_\mu, i.e. it separates tangent spacetime and 'contorted' spacetime.

Concerning the Cartan equations: the connection is trivial and the curvature 0, therefore the first Cartan equation is satisfied. As for the second, which involves the torsion, we do not use explicitly the torsion in our formulation,
we only use, separately, the inertial and the dynamical frame. But if one wishes one can define it, see eq.(17) of the attached file. Since the second Cartan equation is a consequence of the torsion's definition in terms of frame, it is automatically satisfied.

The above is a short summary. In a attached file we describe in detail all this, with the necessary formulas and comments.

The version of our papers conain changes in blue and a new bibliography.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I recommend accepting this article in its present form.