High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

Round 1

Reviewer 1 Report

This is a good paper, quite well written.

Author Response

We would like to gratitude Reviewer 1 for reading and revising the manuscript

Reviewer 2 Report

The paper implements the spinor-helicity formalism to analyze the on-shell structure of the S-matrix of maximally supersymmetric Yang-Mills theories in the planar limit, in dimensions 6,8,10. These theories are known to be non-renormalizable, and the aim of the paper is to give a systematic treatment of UV divergences using the power of the spinor-helicity formalism. 

The paper is well-written, the structure is clear and the results reflect the statements of the abstract and introduction.

I found one typo, at the beginning of p. 10, "The calculate the amplitude" -> "To calculate the amplitude".

Author Response

Reviewer 2 pointed out the typo in the manuscript which is given in Errata. We are also grateful for
this.

Errata

1. The phrase 'The calculate the amplitude" on p.10 is replaced by "To calculate the amplitude"
2. More explicit notation on the Fig.5, Fig.7 and Fig.9

Reviewer 3 Report

In this paper the authors study the UV behavior of gauge theories in higher dimensions. Specifically they concentrate on gauge theories in 4k + 2 and 4k dimensions for k = 1, 2. It is well known that gauge theories in 4 dimensions (i.e the case with k  = 1) can be UV finite whereas in higher dimensions UV divergences should show up. For different values of k, the authors get expected answers using spinor-helicity technique in the planar limit. The advantage I see using spinor-helicity technique is that the UV divergences may be enumerated systematically. The authors elaborate the story in great details, and although the end result justifies the means, this is what one would have expected. My question then lies on a different aspect of the story: we know that gauge theories in 4k + 2 dimensions (especially for k = 2) have anomalies, so they are already not consistent, unless they are coupled to some other theories. For example D = 10 SYM has to be coupled to supergravity to form a consistent set-up. What do the analysis of the authors have to say regarding these kinds of inconsistencies?  

Author Response

Answering the question of Reviewer 3, we assume that as for the possible inconsistency of D=10
theory due to anomalies our analysis seems to be insensitive to these matters at least on the level
of four point amplitude since the anomaly diagrams in D=10 theory contain 6 external legs. It is
not actually clear how possible anomalies manifest themselves within the spinor-helicity formalism
which we use in our paper. But anyway, we would to thank Reviewer 3 for the interesting
discussion topic.