Deconstructing S-Duality

We thank both referees for their feedback and are glad they find our paper interesting and nice to read. Following the suggestions of referee 2 we made the changes outlined below.

1 - In order to minimize the use of acronyms we removed all use of "HM" and made sure that the remaining acronyms are only used within equations (where we find them unavoidable) or when referring to equations, e.g. (BP) and (aBP) are names of equations and we do find it easier to read these letter labels rather than always referring to them by equation number.

2 - We are certainly sympathetic to the notion that when going between dimensions, the amount of supersymmetry is often better characterized by giving the total number of supercharges rather than using the "N =" counting of spinors. We had already paid tribute to this with our footnote 1, which translates the two most common players in our paper, N=4 SUSY in d=3+1 and d=2+1 into 16 and 8 supercharges respectively. To make sure all supersymmetries we use are at least once translated into this language, we added a few words after the first time we mention N=8 SUSY in 2+1 dimensions (which is also a 16 supercharge theory). While mostly using the "N=" notation throughout our paper, we now have every single theory we use defined in the language of total supercharges as well.

3 - We added a reference to the Hill, Pokorski and Wang paper when first discussing using linear sigma models for the purpose of deconstruction.