The Second Superstring Revolution was, like most revolutions, a somewhat messy affair, with a number of pivotal steps along the way: understanding the role of membranes in 11-dimensional supergravity, the discovery of dualities in supersymmetric gauge theories, Polchinski’s appreciation of D-branes as dynamical extended objects in string theory, and of course Maldacena’s formulation of the AdS/CFT correspondence. But perhaps the high point was Ed Witten’s formulation of M-Theory in 1995. And I just noticed that Witten sharing it with the world was captured on video.

Here is Witten’s paper:

String Theory Dynamics In Various Dimensions
Edward Witten

The strong coupling dynamics of string theories in dimension d≥4 are studied. It is argued, among other things, that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring, and that a recently conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions and implies S duality for both heterotic and Type II strings.

Before this result, we knew about five different kinds of string theory, each living in ten dimensions: Type I, two different Type II’s, and two different “heterotic” theories. Then there was the most symmetric form of supergravity, living in 11 dimensions, which some people thought was interesting but others thought was a curiosity that had been superseded by string theory. To everyone’s amazement, Witten showed that all of these theories are simply different limiting cases of a single underlying structure. Nobody knows what that underlying theory really is (although there are a few different formulations that work in some contexts), but we know what to call it: M-theory.

Now Amanda Gefter, author of the new book Trespassing on Einstein’s Lawn (and a recent guest-blogger at Cocktail Party Physics), takes to Twitter to point out something I wasn’t aware of: a video record of Witten’s famous 1995 talk at USC. (I’m pretty sure this is the celebrated talk, but my confidence isn’t 100%.) [Update: folks who should know are actually saying it might be a seminar soon thereafter at Stony Brook. Witten himself admits that he’s not sure.] It’s clearly a recording by someone in the audience, but I don’t know who.

Most physics seminars are, shall we say, not all that historically exciting. But this one was recognized right away as something special. I was a postdoc at MIT at the time, and not in the audience myself, but I remember distinctly how the people who were there were buzzing about it when they returned home.

Nature giveth, and Nature taketh away. The 1995 discovery of M-theory made string theory seem more promising than ever, to the extent that just a single theory, rather than five or six. Then the 1998 discovery that the universe is accelerating made people take more seriously the idea that there might be more than one way to compactify those extra dimensions down to the four we observe — and once you have more than one, you sadly end up with a preposterously high number (the string theory landscape). So even if there is only one unifying theory of everything, there seem to be a bajillion phases it can be in, which creates an enormous difficulty in trying to relate M-theory to reality. But we won’t know unless we try, will we?

Been falling behind on my favorite thing to do on the blog: post summaries of my own research papers. Back in October I submitted a paper with two Caltech colleagues, postdoc Stefan Leichenauer and grad student Jason Pollack, on the intriguing intersection of effective field theory (EFT) and cosmological large-scale structure (LSS). Now’s a good time to bring it up, as there’s a great popular-level discussion of the idea by Natalie Wolchover in Quanta.

So what is the connection between EFT and LSS? An effective field theory, as loyal readers know, an “effective field theory” is a way to describe what happens at low energies (or, equivalently, long wavelengths) without having a complete picture of what’s going on at higher energies. In particle physics, we can calculate processes in the Standard Model perfectly well without having a complete picture of grand unification or quantum gravity. It’s not that higher energies are unimportant, it’s just that all of their effects on low-energy physics can be summed up in their contributions to just a handful of measurable parameters.

In cosmology, we consider the evolution of LSS from tiny perturbations at early times to the splendor of galaxies and clusters that we see today. It’s really a story of particles — photons, atoms, dark matter particles — more than a field theory (although of course there’s an even deeper description in which everything is a field theory, but that’s far removed from cosmology). So the right tool is the Boltzmann equation — not the entropy formula that appears on his tombstone, but the equation that tells us how a distribution of particles evolves in phase space. However, the number of particles in the universe is very large indeed, so it’s the most obvious thing in the world to make an approximation by “smoothing” the particle distribution into an effective fluid. That fluid has a density and a velocity, but also has parameters like an effective speed of sound and viscosity. As Leonardo Senatore, one of the pioneers of this approach, says in Quanta, the viscosity of the universe is approximately equal to that of chocolate syrup.

So the goal of the EFT of LSS program (which is still in its infancy, although there is an important prehistory) is to derive the correct theory of the effective cosmological fluid. That is, to determine how all of the complicated churning dynamics at the scales of galaxies and clusters feeds back onto what happens at larger distances where things are relatively smooth and well-behaved. It turns out that this is more than a fun thing for theorists to spend their time with; getting the EFT right lets us describe what happens even at some length scales that are formally “nonlinear,” and therefore would conventionally be thought of as inaccessible to anything but numerical simulations. I really think it’s the way forward for comparing theoretical predictions to the wave of precision data we are blessed with in cosmology.

Here is the abstract for the paper I wrote with Stefan and Jason:

A Consistent Effective Theory of Long-Wavelength Cosmological Perturbations
Sean M. Carroll, Stefan Leichenauer, Jason Pollack

Effective field theory provides a perturbative framework to study the evolution of cosmological large-scale structure. We investigate the underpinnings of this approach, and suggest new ways to compute correlation functions of cosmological observables. We find that, in contrast with quantum field theory, the appropriate effective theory of classical cosmological perturbations involves interactions that are nonlocal in time. We describe an alternative to the usual approach of smoothing the perturbations, based on a path-integral formulation of the renormalization group equations. This technique allows for improved handling of short-distance modes that are perturbatively generated by long-distance interactions.

As useful as the EFT of LSS approach is, our own contribution is mostly on the formalism side of things. (You will search in vain for any nice plots comparing predictions to data in our paper — but do check out the references.) We try to be especially careful in establishing the foundations of the approach, and along the way we show that it’s not really a “field” theory in the conventional sense, as there are interactions that are nonlocal in time (a result also found by Carrasco, Foreman, Green, and Senatore). This is a formal worry, but doesn’t necessarily mean that the theory is badly behaved; one just has to work a bit to understand the time-dependence of the effective coupling constants.

Here is a video from a physics colloquium I gave at NYU on our paper. A colloquium is intermediate in level between a public talk and a technical seminar, so there are some heavy equations at the end but the beginning is pretty motivational. Enjoy!