More than just strings
Another surprising revelation was that superstring
theories are not just theories of one-dimensional objects. There
are higher dimensional objects in string theory with dimensions from
zero (points) to nine, called p-branes.
In terms of branes, what we usually call a membrane would be a two-brane,
a string is called a one-brane and a point is called a zero-brane.
What makes a p-brane? A p-brane is a spacetime
object that is a solution to the Einstein equation in the low energy
limit of superstring theory, with the energy density of the nongravitational
fields confined to some p-dimensional subspace
of the nine space dimensions in the theory. (Remember, superstring theory
lives in ten spacetime dimensions, which means one time dimension plus
nine space dimensions.) For example, in a solution with electric charge,
if the energy density in the electromagnetic field was distributed along
a line in spacetime, this one-dimensional line
would be considered a p-brane with p=1.
A special class of p-branes in string theory are called D branes.
Roughly speaking, a D brane is a p-brane where the ends of open strings
are localized on the brane. A D brane is like a collective excitation
These objects took a long time to be discovered
in string theory, because they are buried deep in the mathematics of
T-duality. D branes are important in understanding black holes in string
theory, especially in counting the quantum states that lead to black
hole entropy, which was a very big accomplishment for string
How many dimensions?
Before string theory won the full attention
of the theoretical physics community, the most popular unified theory
was an eleven dimensional theory of supergravity, which is supersymmetry
combined with gravity. The eleven-dimensional spacetime was to be compactified
on a small 7-dimensional sphere, for example, leaving four spacetime
dimensions visible to observers at large distances.
This theory didn't work as a unified theory
of particle physics, because it doesn't have a sensible quantum limit
as a point particle theory. But this eleven dimensional theory
would not die. It eventually came back to life in
the strong coupling limit of superstring theory in ten dimensions.
How could a superstring theory with ten spacetime
dimensions turn into a supergravity theory with eleven spacetime dimensions?
We've already learned that duality relations between superstring theories
relate very different theories, equate large distance with small distance,
and exchange strong coupling with weak coupling. So there must be some
duality relation that can explain how a superstring theory that requires
ten spacetime dimensions for quantum consistency can really be a theory
in eleven spacetime dimensions after all.
Since we know that all string theories are related,
and we suspect that they are but different limits of some more fundamental
theory, then perhaps that more fundamental theory exists in eleven spacetime
dimensions? These question bring us to the topic of M
The theory currently known as M
Technically speaking, M
theory is is the unknown eleven-dimensional theory whose low
energy limit is the supergravity theory in eleven dimensions discussed
above. However, many people have taken to also using M
theory to label the unknown theory believed to be the fundamental
theory from which the known superstring theories emerge as special limits.
We still don't know the fundamental M theory,
but a lot has been learned about the eleven-dimensional M theory and
how it relates to superstrings in ten spacetime dimensions.
In M theory, there are also extended objects,
but they are called M branes rather
than D branes. One class of the M branes in this theory has two space
dimensions, and this is called an M2 brane.
Now consider M theory with the tenth space dimension
compactified into a circle of radius R. If one of the two space dimensions
that make up the M2 brane is wound around that circle, then we can equate
the resulting object with the fundamental string (one-brane) of type
IIA superstring theory. The type IIA theory appears to be a ten dimensional
theory in the normal perturbative limit, but reveals an extra space
dimension, and an equivalence to M theory, in the limit of very strong
We still don't know
what the fundamental theory behind string theory is, but judging
from all of these relationships, it must be a very interesting and rich
theory, one where distance scales, coupling strengths and even the number
of dimensions in spacetime are not fixed concepts but fluid entities
that shift with our point of view.