The authors of the paper have chosen to use N=4 topology, or supersymmetry in 4 dimensions, to simplify modeling how black holes with multiple centers decay.

In these special cases the mock modular forms, described by Ramanujan on his death bed in 1920 before anyone was talking about black holes, provide a counting function to describe the black hole's world line in string theory. In other words, they can model what's happening inside the black hole.

Using the mock modular forms was attractive because it satisfies the desire to use the holography theories about black holes to model what happens to information as matter crosses the event horizon.

The authors further justify their choice by explaining how modular forms are already used to describe characteristics of black holes in string theory, such as its Fourier coefficients (component waves) and how they change as an object crosses the wall.

The difference between a mock modular form and a modular form is that a modular form is holomorphic is differentiable at all points in Real space at infinity. A mock modular form is meromorphic, it is differentiable at almost all points in Real space at infinity. The authors account for their counting function being meromorphic by introducing a 'shadow' factor.

Edit: in particular they are complex differentiable. Wikipedia has a nice image where you can see a meromorphic function conforming to space and then a few spots where it jumps (is not continuous). A holomorphic function would conform smoothly all over. http://en.wikipedia.org/wiki/Meromorphic_function

Here's a link to a paper on this: http://arxiv.org/abs/1208.4074. Explaining it is well beyond my capacity, though.

For a layman the abstract sounds like a computer-generated hoax.

You could say that about any field that one is unfamiliar with. Heck, the most basic art concepts could seem like so to a blind man. Mathematicians have worked for ages on simplifying the concepts so every term is there because it helps a trained mathematician understand what is going on.

It seems genuine, or at least more sophisticated than computer-generated abstracts usually are. It seems to repeatedly mention the same concepts which is something usually lacking in computer-generated abstracts, though it does mix seemingly tenuously related topics.

I have no idea what any of it means though.

The abstract, although it's also far beyond me, actually sounds even more impressive than the article lets on.

Modern mathematicians find it useful for calculating properties of black holes. Ramanujan had no more to do with black holes that, say, Newton who invented calculus after all, and that's used for black-hole describing too. Its kind of a meaningless fact to toss into the article.