Chern–Simons States in SO(1,n)Yang–Mills Gauge Theory of Quantum Gravity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with a Yang-Mills theory based on the gauge group SO(1,n). The model is renormalizable and has been shown in the literature to be a candidate for a UV complete unified theory of all interaction including gravity. 
The paper discusses the effect of the  Chern-Simons (CS) term entering in the Lagrangian
of these models. The CS term is a total divergence that does not affect perturbative computations but enforces non-trivial background state configurations in the theory. These configurations are  characterized by suitably defined topological invariants.

The paper then presents a construction of such CS states in the WKB approximation  
and computes some sample correlation functions, obtained by an expansion around such states
in leading order approximation.

Before publication I would recommend that the Author takes into account the following points in order to help the reader to better understand the paper:

i) no mention is made to matter fields in the manuscript. It is well-known in the literature that the matter field content of the theory depends on the particular gauge group SO(1,n) chosen. The Author should discuss which groups are candidates to reproduce the Standard Model field content plus some extra fields (e.g. in connection with the so-called mirror fermions problem).
Comments on the impact of the CS states on the fermion correlators, if any, would also be very useful.
ii) the Author should discuss the physical meaning of the correlators in the presence of the CS states. Do these states affect the in- and out- states of the theory? How is the S-matrix defined (via the usual Gell-Man and Low formula or in some other ways)? 

Once these points have been taken into account in my opinion the paper can be accepted for publication.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This is a nice paper and deserves publication. 

Author Response

Thank you for an acceptance of my paper

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, 

the authors consider a generic SO(n,1) group claiming that this may potentially unify all interactions, including gravity. This idea deserves interest but it is certainly not new, since proposed back in the days by several authors, inspired for example by the work of McDowell and Mansouri (MM) also mentioned by the authors. I find several problems in the approach proposed by the authors, which are not clarified in this paper. First, I do not understand why the authors insist to separate tetrads and spin connection, which, for example, in MM, are unified in a unique gauge connection A_{\mu}^{AB}, with A,B indices of SO(4,1). Second, from recent studies, there are several updates on the subjects that the authors do not consider at all: 1) MM generate a classical bare \Lambda and M_{Pl} (cosmological constant and Planck scale from original parameters of the lagrangian) and this consideration seems completely absent in this paper while crucially important; 2) the authors did not clarify if they start from a Minkowski background, which will be a background dependent quantum gravity perturbative approach, or if they assume a pre-geometric gravity prospective starting from a more primitive topological space-time; 3) the authors do not explain if they wish to unify the forces embedding for example SO(4,1)xSO(10) to SO(14,1). if so, anyway, this is not enough to show the unification of all the coupling constants of all the fundamental forces (and anyway this idea is not new at all, many authors proposed it before without completing it). Finally many references are missing, including the approach proposed by Frank Wilczek, trying to re-interpret gravity as emergent from a spontaneous symmetry breaking mechanism starting from a SO(4,1) or SO(3,2) MM model with a new scalar field. Without these clarifications or at least comments on recent updates in the subject, this paper cannot be accepted. 

Author Response

Please see the attachment

Author Response File: Author Response.pdf