A Borcherds-Kac-Moody superalgebra with Conway symmetry
In this paper an interesting Borcherds-Kac-Moody (BKM) algebra is constructed, which is expected to be a particular realization of an algebra of BPS states in string theory. This statement already asserts that the paper is of interest to both mathematicians and physicist; however, to fully comprehend it, relevant background in mathematics and physics is required. More precisely, the algebra that the authors construct is an infinite-dimensional Lie superalgebra with Conway symmetry; it is analogous to the monstrous BKM algebra constructed originally by Borcherds. This algebra is expected to be related to cohomological Hall algebras, which have been independently argued to provide a natural realization of algebras of BPS states, and other related topics, such as motivic Donaldson-Thomas invariants, automorphic forms, vertex algebras, etc. A construction of an explicit, non-trivial example that enables to illustrate all such links is an important motivation for this paper. Another motivation is a generalization (or providing other examples) of the relation between the moonshine and string theory. In this context, the authors find that the algebra they construct is indeed an interesting example that plays a role in the so called Conway moonshine, and they indicate that from this perspective it should also have an interpretation of an algebra of BPS states. The paper is interesting and clearly written. However, to fully understand it, a reader should be familiar with vast background, which includes string theory, BPS states, BKM (super)algebras, moonshine, etc. Some properties of BKM superalgebras are briefly summarized in an appendix, which is quite helpful; however readers unfamiliar with other topics should consult other sources. Nonetheless, the paper can be recommended both to experts in this area, as well as to non-experts, who are looking for inspiration and an interdisciplinary area of research.
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