BPS spectrum, wall crossing and quantum dilogarithm identity (Q346012)

This rather lengthy (\(\approx\) 100 pages + appendices) compilation might be inaccessible for readers who are unfamiliar with the topic of BPS spectra, as many basic ingredients like the notion of a BPS spectrum itself is never explained during that tract. In addition, many simple language mistakes make the article unpleasant to read and very often the meaning of a certain line of argument stays unclear.NEWLINENEWLINEThe paper starts with an introduction to the topic and the definition of ``green mutation sequences'' that will be used later on. In the following review, chambers and quivers are introduced and expanded in the section on quiver representation theory. Apparently, ``green'' and ``red'' refers to the coloring of nodes in the diagrams presented in some figures of the paper, a fact that may cause trouble for readers having problems to distinguish those colors.NEWLINENEWLINEIn the course of the paper, BPS spectra for ``\(A_1\)'' and ``\(A_{N-1}\) theory'' are derived and presented, where, unfortunately neither \(A_1\) nor \(A_{N-1}\) theory is explained but rather referenced to the literature listed (the first reference already gives a good explanation). A vast amount of figures and diagrams try to picturize what is going on. The expert reader may appreciate the achievements made in this work, for the non-expert it is not advisable to have a look inside.