To close the year, my collaborators (Juan Abranches and Reiko Toriumi)and I just posted our new manuscript “An equivalence in random matrix and tensor models via a dually weighted intermediate field representation“.

The story of how we arrived here made me think of a question I’ve been asked for my whole career: what is quantum gravity useful for? Well, this work started when we were thinking about ways to study quantum spacetime with a time direction. All of us had previously worked on a toy model in two dimensions that exactly does this by gluing triangles to construct two-dimensional spacetime. The key to introducing a time direction is in gluing triangles following very specific rules.

In the cases of 3 and 4 dimensions the question is: what are the ‘right rules’ to build spacetimes that resemble our universe? Trying to answer this question using the tool of Random tensor models, led us to discover (and prove) very interesting equivalences between, in principle, very different mathematical models. And even though we haven’t fully answered our initial question, we trust these results will be very useful to advance in this direction, but also open new avenues of research in mathematics.