The world as a stringy hologram, or the biggest development in theoretical Physics of the last 25 years

About the author

Hi everyone! My name is Nathan Haouzi, I am a current member at the School of Natural Sciences at the Institute for Advanced Studies at Princeton. Before that, I was a postdoctoral researcher for three years at the Simons Center for Geometry and Physics. I hold a graduate degree in Physics from UC Berkeley, and two undergraduate Bachelors degrees in Mathematics and in Physics from MIT. These days, I spend my time thinking about various questions at the intersection of Mathematics and theoretical Physics, and write research papers about it. I have also been teaching those subjects at all levels for more than 10 years, mostly in an academic setting.

I am a big fan of the 3blue1brown channel, I strongly believe we need quality science content out there! My biggest problem with the state of YouTube is that the content is either very specialized recorded lectures for an academic audience, or a plethora of videos at the highschool/undergraduate/early graduate level. The topics covered are usually interesting, but a little outdated or far removed from what is actually discussed in a research setting. I feel SoMe2 may be the perfect opportunity to present more actual topics!

Quick Summary

Sorry about the (only slightly) clickbaity title. While at Harvard, Maldacena came up with a groundbreaking and elegant correspondence in 1997, which rocked the Physics world. Roughly, it says that you can think of the standard model of particle Physics in our usual flat (3+1)-dimensional spacetime equally well as a theory of strings in one higher dimension, in a universe with a slightly different "hyperbolic" geometry. To this day, Maldacena's 20 page paper "The Large N limit of superconformal field theories and supergravity" is the most quoted paper in all theoretical physics (per InspireHEP data), with over 17,000 citations and still rising. The history leading to Maldacena's result is long and fascinating, starting in the 70's with the discovery of confining strings in the standard model by Wilson, and then in the 90's with the formulation of the holographic principle by t’ Hooft and Susskind, the discovery of D-branes by Polchinski, the realization that 5-dimensional strings can describe the standard model by Polyakov... And let's not forget Witten who explained in 1998 how all of it fits together!

Here, the objective of the video would be modest: we will give a taste of what the holographic principle means, and show without any hard math that a world like ours but with a large number of gluon particles is equivalent to a theory of strings. The standard model only has 8 gluons, the idea will be to replace 8 by a very large number and see what happens (this number of gluons is the "N" in Maldacena's paper). With that replacement, a lot of the usual complications and painful subtleties of gauge theory disappear, and we will be able to show that our theory can equally well be described by a theory of strings in 5 dimensions.

Target medium

The idea is to make a video which is anywhere between half an hour long to slightly less than an hour long. Ideally closer to the half hour mark. The target level is early undergraduate STEM level. A lot of the parts will only require a highschool algebra level.

I have no experience in animation, and am open to suggestions as to what would work best to illustrate the concepts in the video. We will need to display various Feynman diagrams, some simple surfaces like a sphere, a torus, a hyperboloid, some squiggly lines representing particles or strings... and a bunch of equations. The equations will need to be animated, with terms that will be added or removed in sync with the voice of the narrator, various color codes and so on. Nothing fancy, but I would love it to be aesthetically pleasing to look at as much as possible.

The Math and Physics requirements will be minimal... In particular, no knowledge of Yang-Mills gauge theory or string theory will be assumed or needed. We may have to take the derivative of a function at some point in the video, but that's basically it as far as calculus is needed. We will assume knowledge of elementary highschool algebra, and the main math tool we will use will be counting the number of loops or crossing lines in some easy graphs. Near the end of the video, we may need to convey the idea of a "metric" like one would learn in a special relativity undergraduate class. I am not sure about that last point yet. I think we could motivate what a metric is rather easily in 5 minutes or so. Creative Ideas on how to do that using animations are more than welcome.

More details

The video outline is pretty straightforward:

1) We will explain how to count Feynman diagrams, or various scattering processes, in the standard model of particle physics with many gluons. This will be a fun exercise where we build our intuition from the ground up by playing with many examples and understand there is a pattern that is easy to write down.

2) We will then explain how to count scattering processes in a theory of strings instead of particles. We will be led to the amazing realization that we are basically doing in a different language the counting of point 1) ! In particular, the parameter that sets the strength of string interactions is related to the number of gluons in the standard model.

3) We will briefly motivate the need for an extra dimension for the strings to live in, hence the name "hologram" that shows up in this story.

4) We will give a two-line qualitative proof of the remarkable prediction that under some mild extra assumptions, the strings really live in a hyperbolic space in five dimensions, the essence of Maldacena's result.

The major punchline is in 2), what follows after that is profound but may need to be cut short not to make the video too long.

Contact details

Feel free to email me at nathanh@ias.edu . We can discuss details and logistics if you are interested.

leios / SoME_Topics