Maybe let me start broadly. I work on String Theory. Traditionally, this area of research has been focused on string theory being the so-called "Theory of Everything," (TOE). What this grand statement means is NOT that if I understand string theory, then I can predict everything in the world. Rather, string theory is meant to be the ultimate reductionist theory (meaning smallest, most fundamental - i.e., originally atoms were the fundamental things, then we discovered protons and neutrons as more fundamental, then quarks are still more fundamental, etc.). String theory says that ALL the forces of nature - Electromagnetism, Strong Force (holding protons/neutrons together), Weak Force (making nuclear decay happen) and Gravity, each of which traditionally needs to be treated separately - come from ONE theory which describes how each of them work. This is great, and is really interesting, but it has been going on for almost 30 years, and it still hasn't come out quite right. In fact, right now, there is controversy over this research direction, made public in books by Peter Woit and Lee Smolin. They both have valid points that I agree with, but I think they miss some of the overall picture. Although perhaps that isn't fair of me, as I haven't read either of their books. Someday...
However, this is not the direction that I'm working in. It is definitely related very strongly, but the focus of it is not so much placed on having string theory being the TOE, but rather on using string theory to say interesting things about OTHER subjects. This goes under the broad category of "the Anti de-Sitter Space/Conformal Field Theory Correspondence," or as it is referred to, the
So, what is this correspondence, you ask? Excellent question! It's a little like Voodoo. Start with two, a priori TOTALLY unconncected theories (here string theory in AdS space vs. what is known as a conformal field theory).
(Side note: What do I mean when I say "you have such-and-such a theory"? A theory is a set of rules that tell you how objects move around. So, for example, one theory is electromagnetism - there are charged things around, and there are rules as to how they move when you apply electricity to them. There are more technical definitions of what makes something a theory rather than BS, but this is good enough for what I mean.)
Ok, so back to the two unconnected theories. The analogy is to Voodoo, where you have a voodoo doll that you can stick pins in. And just like with Voodoo, these things shouldn't have anything to do with one another, but it turns out that everything you do to one of the things (say stick a pin in the doll) corresponds exactly to doing a similar thing to the other (equivalent to sticking a sword in the person, or whatever). AdS/CFT is very similar - every object in one theory has a corresponding object in the "dual" theory. And if the rules of theory A tell you that object A should move just so, then it will happen that the rules of theory B tell you that... yep, object B should move in just the same way.
Ok, so this is really vague and weird, so what do you actually mean, Alex? Let me be a bit more specific. What do I mean when I say "string theory in AdS space"? Just that it involves the strings of String Theory are moving around in a particular gravity set up (AdS space is just the name of the particular gravity set up). So just like you can imagine strings moving under the gravitational influence of the sun, say, you can imagine strings moving under the influence of gravity in some other set up. Obviously, this satisfies what I said about theories - there are objects, and there are rules.
Ok, so what do I mean by "conformal field theory"? Basically this is referring to a set of rules like nuclear physics has, involving quarks, gluons, and other elementary particles that we can do experiments on. So in this theory, there are objects (quarks, gluons, etc.) and there are the rules that tell you how they move about.
So why do we care? There are essentially two reasons why this is cool:
- The nuclear physics stuff happens in the normal number of spacetime dimensions - there are three spatial dimensions and one time. The string theory stuff all happens, however, in ten dimensions (meaning that strings can move not only up/down, right/left, forward/backwards, but also in six other directions!). And somehow, these two theories must be totally equivalent. In particular, if the string moves in one of these other crazy directions, what would that look like in the nuclear theory, where things can only move in the normal three? This is cool, and is a generally very interesting area of physics called "holography" (like holograms, which look like they have more dimensions than they actually do (three rather than two).
- In this AdS/CFT, in general, we know how to calculate the rules in one of the theories, but not in the second. So this duality is potentially really useful to be able to tell us the answer to rules that we otherwise DON'T KNOW HOW TO CALCULATE! That is also cool.
So, this is the broad outline of what I'm doing. Maybe next time I'll go into a bit more detail about what exactly I'm calculating in one of these theories. Let me know if any of this stuff is understandable/interesting.