What's the current answer
to the question, "What is string theory?"
Well, we've understood somehow that there's a more unified picture that
mixes up quantum mechanical effects controlled by hbar and string effects
controlled by alpha prime. So, there's this M theory story where different
string theories are mixed up by dualities. I can't claim that we've gotten
to the bottom of it, though.
What is M theory?
M theory is a name
for a more unified theory that has the different string
theories, as we know them, as limits, and which also can reduce, under
appropriate conditions, to elevendimensional supergravity. There's this
picture that we all have to draw where different string theories are limits
of this M theory, where M stands for Magic, Mystery or Matrix, but it
also sometimes is seen as standing for Murky, because the truth about
M theory is Murky. And the different limits, where the main parameter
simplifies, give the different string theories  Type IIA, Type IIB,
Type I, and there's elevendimensional supergravity, which turns out to
be an important limit even though it isn't part of the systematic perturbation
expansion, then there's the E8XE8 heterotic string, and there's SO(32)
heterotic string.
So Mtheory is a name
for this picture, this more general picture that will generate the different
limits through the different string theories. The parameters in this picture
we can think of being roughly hbar, which is Planck's constant, and that
determines how important the quantum effects are, and the other parameter
is alpha prime, which is the tension, related to the tension of the string,
that determines how important stringy effects are. So traditionally, a
physicist looking at Type IIA, for example, by traditional weak coupling
methods, explores this little region, and if asked how his theory is related
to Type I theory, the answer would have to be, "Well I don't know,
that's something else."
And likewise, if you
ask this observer what happens for strong coupling, the traditional answer
was, "Well I don't know." In graduate courses, you learn that
you can do more or less anything for weak coupling, but you can't do anything
for strong coupling. What happened in the 90s was that we learned how
to do a little bit for strong coupling, and it turned out that the answer
is Type IIA at strong coupling turns out to be Type I in a slightly different
limit, SO(32) heterotic, and so on. So we built up this more unified picture,
but we still don't understand what it means
What is K theory and what does it mean for string
theory?
K theory is a mathematical theory that studies topology using matrices,
using operators that don't commute with each another. What topology
is, first of all, is the branch of mathematics where you don't care
about the shape, so for example, a lumpy ball is equivalent to a round
ball. But if there are holes, you do care about that, so a donut is
different from either of these two. So, mathematicians learned, around
1960, that there was a very powerful tool in topology based on matrices,
and that tool was K theory. And since quantum mechanics is about noncommuting
operators, or matrices, there has always been a kind of naive analogy
between K theory and quantum mechanics. An analogy that seemed naive
to most physicists, but was often drawn by mathematicians such as Michael
Atiyah.
However, we learned
in the last few years that some questions about string theory, but slightly
specialized questions usually, are usefully addressed using K theory.
What K theory really addresses is a little bit subtle to explain. If
you want to understand the charges carried by the Dbranes, that's a
question that leads to K theory. Or I might say at an even more basic
level, Dbranes are these strange objects whose positions are measured
by matrices, and studying those matrices leads to K theory.
So K theory is the
sort of topological underpinning of Dbrane theory. But as physicists
we're interested very much in whether the ball is round or lumpy, as
are different things in physics. We wouldn't want to play baseball with
a lumpy ball. So, the topology is just one side of the story..
What is noncommutative geometry and why is it
important in string theory?
Well, one thing which we know about for sure in string theory is that
the ordinary classical ideas about geometry are approximations, and
don't really work precisely. But what you should really replace them
with is not clear. However, there's a naive ideas about strings which
really only works for open strings. Open strings are strings with endpoints,
like in the original Type I superstring, where a particle was represented
by a piece of string with charges at the ends. I've labeled the charges
as q and qbar for quark and antiquark, but that's modern terminology
that might not have been present in the early says of string theory.
Once you've got
open strings, they can join together, I'm going to call my open strings
A or B, and they join end to end. But there are two ways of joining
them. I could join them with A on the left and B on the right, or I
could join them with B on the left and A on the right, and I get two
different outputs. And it's very much like taking two matrices A and
B and multiplying them together. So there's some noncommutativity in
the interactions.
And when you take
account of the fact that string theory is all about geometry, somehow
this is geometry where noncommutative objects are built in. In fact
I've mentioned now a couple portions of it. There's the noncommutativity
of joining strings, and there's the matrices that don't commute, which
are related to K theory and also to the Dbrane positions and so on.
Anyway, coming back
here, you can try to systematically describe open string physics at
least in terms of noncommutative ideas introduced in geometry,and you
can get a general answer of some kind, but it's rather abstract and
very hard to use. However, in the last couple of years, it was discovered
that there's a certain limit with a very strong background magnetic
field in which things simplify, and you can actually say something simple
and useful based on the noncommutative geometry. That's a case where
the rather abstract and hard to use noncommutative geometrical concepts
actually come down to Earth and become useful.
Why is it so hard to break supersymmetry in
string theory?
Well, if I knew the answer, if I knew how Nature has done supersymmetry
breaking, then I could tell you why humans had such trouble figuring
it out. But I can say one thing about it. When supersymmetry is not
broken, it's easy to get a zero cosmological constant in string theory.
And although a zero cosmological constant might not be the truth, it's
incredibly close to the truth. If you break supersymmetry, if you do
it the wrong way, you're going to get a cosmological constant that's
much too big, and then you may well get associated problems, such as
instabilities, runaways and so on. So it's easy to find ways that string
theory could break supersymmetry, but they all have bad consequences.
So I assume we're missing something, which is the answer to your question.
How can the cosmological constant be so close
to zero but not zero?
I really don't know. It's very perplexing that astronomical observations
seem to show that there is a cosmological constant. It's definitely
the most troublesome, for my interests, definitely the most troublesome,
observation in physics in my lifetime. In my career that is.
What has been the most surprising or interesting
thing that you have learned in physics?
I'm going to interpret the question to be what's the most interesting
thing I've learned in my career, whether I discovered it or not. It's
something I've learned, perhaps through the work of other people or
from textbooks. So in that sense, the most surprising thing I've learned,
even though I had nothing to do with discovering it, is that strings
can describe quantum gravity.
What has been the most surprising or interesting
thing that you have learned in science outside of physics?
Well it's not that amazing that to me, a lot of science is physics.
So, for example, I can't give you an answer in terms of chemistry, because
physics underlies chemistry. I could give you an answer in biology.
Biologists have learned lots of wonderful things. But it's hard to properly
maintain one's sense of wonder about them, for some things that were
known so long that we all remember so little that we take them for granted.
But there's the theory of evolution, which is an amazing insight. And
there's the understanding of the genetic code, that's a marvelous insight.
Of course, if we
move on to math, which you might think isn't physics, but which is much
closer to what I know, then there are lot's of fun and exciting things
there. I hardly know what to tell you because, again, there are lots
of things that are really wonderful but which we take for granted because
it's all known. Like there's calculus. Calculus is pretty amazing.
But... it's not
the first thing that comes to mind in answering such a question, because
such a question tends to make you think of more recent discoveries.
But... if I just have to ask , of everything I've ever learned in
math, what's the most amazing and surprising  it might by that calculus
should win the prize, even though it's not so new any more.
