Chiropteral Mirror Symmetry?

Spurred by the previous post showing M-theory’s possible relation to matters Chiropteral, Joe Polchinski (who I think, in 1995 or 1996, first drew the diagram that I messed with in that post) emailed me* to say that there is a quite striking appearance of batman-ology in the string theory literature. It’s from one of the classic Mirror Symmetry papers of 1990 by Candelas, De La Ossa, Green, and Parkes, “An Exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds.” (you can find it via here). Here it is:

What is this? It has to do with spaces in string theory called “Calabi-Yau manifolds”, which are important (in some approaches) as starting points for constructing models of the fundamental particles and interactions in our world, starting with string theory.

The plot is actually a piece of a “metric on moduli space”. It represents the geometry, not of a particular manifold, but on a space of manifolds. The manifolds typically come as part of a large family. Each point on the plot represents a particular manifold in that family. The family is called a “moduli space” and knowing the shape of that space (the distance between various points on that space) is to know the “metric” on that “moduli space”. This is what’s partly shown in the plot. The cusps (bat ears) are special points called “conifold points”.

Mirror symmetry is the (then) surprising relation between apparently totally different CY manifolds that string theory reveals. That paper was presenting a specific example.

As a bonus, while digging into the paper just now, I found another cute bat-shape-related diagram in the paper:

So that I don’t have to do the work, I’ll let you dig into the paper to know what on earth that is, if you’re curious enough.

-cvj

*Thanks Joe!