I believe this bizarre paper is best understood as one of a collection of papers across several disciplines, whose common element appears to be the Slovak physicist Richard Pincak. Basically, there's a new 14-dimensional "theory", "G-theory", which has branes and other features in common with string theory, and which is "applied" not just to particle physics, but also to finance and, here, to molecular biology.

How can you "apply" a quantum geometric theory to bioinformatics? Here is a hint. As most people know, DNA is a polymer consisting of a sequence of nucleotide bases, drawn from an alphabet of four basic types, that are abbreviated A, C, G, T.

Begin with equation 1 in this paper. You will find a mapping in which these four nucleotides are represented by complex quaternions (and apparently the gene that contains them is also represented by an arbitrary complex phase, that's the beta_i appearing in an exponent in those formulas).

Now, jump ahead to page 13. You will find a reference to a "Hopf fibration over DNA molecule". What's going on? The nucleotides have already been mapped to quaternions. So now, the DNA sequence is being mapped to something like a bundle of oriented quaternionic manifolds along a line.

So, I now have some idea how this strange aggregate of ideas could get started. The base-4 sequences of nucleotides can get mapped to a geometric entity, and from there you can add dimensions corresponding to evolution, to chemical binding affinities, to fitness... and you can hope to apply numerous advanced concepts from algebraic geometry.

I strongly doubt that there is much here which makes sense. "Anti de Sitter" is confused with "anti self dual", the specifics of the quaternionic encoding of the nucleotides are introduced without motivation, on page 24 there's crazy talk about retrotransposon reincarnation via anti-ghost fields (I don't know if they just mean the re-expression of a silenced gene, or something weirder). And I've only scratched the surface.

Originally I thought this might be a cynical exercise in using higher-math jargon to create an illusion of science. But I now think it's earnest. In this and its companion papers, there's some real creativity. (For another example, see the title concept in this paper on machine learning.) But all the evidence suggests that it's ultimately incoherent. So I will recommend these papers only for people who like to explore that sort of thing.