In a sense, the introduction of M-theory marks the end of “string theory,” because it ceases to be a theory that contains only fundamental strings. M-theory also contains multidimensional membranes, called branes. Strings are only 1-dimensional objects, and therefore only one of the types of fundamental objects that make up the universe, according to the new M-Theory.
Branes have at least three key traits:
Branes exist in a certain number of dimensions, from zero to nine. Branes can contain an electrical charge.
Branes have a tension, indicating how resistant they are to influence or interaction.
String theory became more complex with the introduction of multidimensional branes. The first branes, called D-branes, entered string theory in 1989. Another type of brane, called a p-brane (not to be confused with the term you used to tease your younger sibling with), was later introduced. Later work showed that these two types of branes were in fact the same thing.
Branes are objects of multiple dimensions that exist within the full 10-dimensional space required by string theory. In the language of string theorists, this full space is called the bulk.
One major reason that string theorists didn’t originally embrace branes was because introducing more elaborate physical objects went against the goal of string theory. Instead of simplifying the theory and making it more fundamental, branes made the theory more complicated and introduced more types of objects that didn’t appear to be necessary. These were the exact features of the Standard Model that string theorists hoped to avoid.
In 1995, though, Joe Polchinski proved that it wasn’t possible to avoid them. Any consistent version of M-theory had to include higher-dimensional branes.
The discovery of D-branes: Giving open strings something to hold on to
The motivation for D-branes came from work by Joe Polchinski, Jin Dai, and Rob Leigh of the University of Texas, and independent work performed at the same time by Czech physicist Petr Horava. While analyzing the equations of
string theory, these physicists realized that the ends of open strings didn’t just hover out in empty space. Instead, it was as if the end of the open string was attached to an object, but string theory at the time didn’t have objects (other than strings) for it to attach to.
To solve this problem, the physicists introduced the D-brane, a surface that exists within the 10-dimensional superstring theory so open strings can attach to them. These branes, and the strings attached to them, are shown in Figure 11-1. (The “D” in D-brane comes from Johann Peter Gustav Lejeune Dirichlet, a German mathematician whose relationship to the D-brane comes from a special type of boundary condition, called the Dirichlet boundary condition, which the D-branes exhibit.)
Figure 11-1:
Open strings attach to the brane at each end. The ends can attach to the same brane or to different branes.
It’s easiest to visualize these branes as flat planes, but the D-branes can exist in any number of dimensions from zero to nine, depending on the theory. A 5-dimensional D-brane would be called a D5-brane.
It’s easy to see how quickly these D-branes can multiply. You could have a D5-brane intersecting a D3-brane, which has a D1-brane extending off of it. Open superstrings could have one end on the D1-brane and the other end on the D5-brane, or on some other D5-brane in another position, and D9-branes (extended in all nine dimensions of space-time) could be in the background of all of them. At this point, it’s clear that it begins to be quite difficult to picture this 10-dimensional space or keep all the possible configurations straight in any meaningful way.
In addition, the D-branes can be either finite or infinite in size. Scientists honestly don’t know the real limitations of how these branes behave. Prior to 1995, few people paid much attention to them.
Creating particles from p-branes
In the mid-1990s, Strominger performed work on another type of brane, called p-branes, which were solutions to Einstein’s general relativity field equations. The p represents the number of dimensions, which again can go from zero to nine. (A 4-dimensional p-brane is called a 4-brane.)
The p-branes expanded infinitely far in certain directions but finitely far in others. In those finite dimensions, they actually seemed to trap anything that came near them, similar to the gravitational influence of a black hole. This work has provided one of the most amazing results of string theory — a way to describe some aspects of a black hole (see the section “Using branes to explain black holes”).
In addition, the p-branes solved one problem in string theory: Not all of the existing particles could be explained in terms of string interactions. With the p-branes, Strominger showed that it was possible to create new particles without the use of strings.
A p-brane can make a particle by wrapping tightly around a very small, curled-up region of space. Strominger showed that if you take this to the extreme — picture a region of space that’s curled up as small as possible — the wrapped p-brane becomes a massless particle.
According to Strominger’s research with p-branes, not all particles in string theory are created by strings. Sometimes, p-branes can create particles as well. This is important because strings alone did not account for all the known particles.
Deducing that branes are required by M-theory
Strongly motivated by Edward Witten’s proposal of M-theory, Joe Polchinski began working intently on D-branes. His work proved that D-branes weren’t just a hypothetical construct allowed by string theory, but they were essential to any version of M-theory. Furthermore, he proved that the D-branes and p-branes were describing the same objects.
In a flurry of activity that would characterize the second superstring revolution, Polchinski showed that the dualities needed for M-theory only worked consistently in cases where the theory also contained higher dimensional objects. An M-theory that contained only 1-dimensional strings would be an inconsistent M-theory.
Polchinski defined what types of D-branes string theory allows and some of their properties. Polchinski’s D-branes carried charge, which meant that they interacted with each other through something similar to the electromagnetic force.
A second property of D-branes is tension. The tension in the D-brane indicates how easily an interaction influences the D-brane, like ripples moving across a pool of water. A low tension means a slight disturbance results in large effects on the D-brane. A high tension means that it’s harder to influence (or change the shape of) the D-brane.
If a D-brane had a tension of zero, then a minor interaction would have a major result — like someone blowing on the surface of the ocean and parting it like the Red Sea in The Ten Commandments. An infinite tension would mean the exact opposite: No amount of work would cause changes to the D-brane.
If you picture a D-brane as the surface of a trampoline, you can more easily visualize the situation. When the weight of your body lands on a trampoline, the tension in the trampoline is weak enough that it gives a bit, but strong enough that it does eventually bounce back, hurling you into the air. If the tension in the trampoline surface were significantly weaker or stronger, a trampoline would be no fun whatsoever; you’d either sink until you hit the ground, or you’d hit a flat, immovable trampoline that doesn’t sink (or bounce) at all.
Together, these two features of the D-branes — charge and tension — meant that they aren’t just mathematical constructs, but are tangible objects in their own right. If M-theory is true, D-branes have the capacity to interact with other objects and move from place to place.
Uniting D-branes and p-branes into one type of brane
Though Polchinski was aware of Strominger’s work on p-branes — they discussed their projects over lunch regularly — both scientists thought that the two types of branes were distinct. Part of Polchinski’s 1995 work on branes included the realization that they were actually one and the same object. At energy levels where predictions from string theory and general relativity match up, the two are equivalent.
It might seem odd that this hadn’t occurred to either of the men before 1995, but there was no reason to expect that the two types of branes would be related to each other. To a layman, they sound basically the same — multidimensional surfaces existing in a 10-dimensional space-time. Why wouldn’t you at least consider that they’re the same things?
Well, part of the reason may be based on the specific nature of scientific research. When you’re working in a scientific field, you are quite specific about the questions you’re asking and the ways in which you’re asking them. Polchinski and Strominger were asking different questions in different ways, so it never occurred to either of them that the answers to their questions might be the same. Their knowledge blinded them from seeing the commonalities. This sort of tunnel vision is fairly common and part of the reason why sharing research is so encouraged within the scientific community.
Similarly, for a laymen, the dramatic differences between these two types of branes are less clear. Just as someone who doesn’t study much religion may be confused by the difference between Episcopalian and Catholic theological doctrines, to a priest of either religion the differences are well-known, and the two are seen as extremely distinct.
In the case of branes, though, the laymen would have had clearer insight on the issue than either of the experts. The very details that made D-branes and p-branes so intriguing to Polchinski and Strominger hindered their ability to see past the details to the commonalities — at least until 1995, when Polchinski finally saw the connection.
Because of equivalence, both D-branes and p-branes are typically just referred to as branes. When referencing their dimensionality, the p-brane notation is usually the one used. Some physicists still use the D-brane notation because there are other types of branes that physicists talk about. (For the remainder of this topic, I mainly refer to them as branes, thus saving wear and tear on my keyboard’s D key.)
Using branes to explain black holes
One of the major theoretical insights that string theory has offered is the ability to understand some black hole physics. These are directly related to work on p-branes, which, in certain configurations, can act something like black holes.
The connection between branes and black holes was discovered by Strominger and Cumrun Vafa in 1996. This is one of the few aspects of string theory that can be cited as actively confirming the theory in a testable way, so it’s rather important.
The starting point is similar to Strominger’s work on p-branes to create particles: Consider a tightly curled region of a space-dimension that has a brane wrapped around it. In this case, though, you’re considering a situation in which gravity doesn’t exist, which means you can wrap multiple branes around the space.
The brane’s mass limits the amount of electromagnetic charge the brane can contain. A similar phenomenon happens with electromagnetically charged black holes. These charges create an energy density, which contributes to the mass of the black hole. This places a limit on the amount of electromagnetic charge a stable black hole can contain.
In the case where the brane has the maximum amount of charge — called an extremal configuration — and the case where the black hole has the maximum amount of charge — called an extremal black hole — the two cases share some properties. This allows scientists to use a thermodynamic model of an extremal configuration brane wrapped around extra dimensions to extract the thermodynamic properties that scientists would expect to obtain from an extremal black hole. Also, you can use these models to relate near-extremal configurations with near-extremal black holes.
Black holes are one of the mysteries of the universe that physicists would most like to have a clear explanation for. For more details on how string theory relates to black holes, skip ahead to topic 14.
String theory wasn’t built with the intention of designing this relationship between wrapped branes and black holes. The fact that an artifact extracted purely from the mathematics of string theory would correlate so precisely with a known scientific object like a black hole, and one that scientists specifically want to study in new ways, was seen by everyone as a major step in support of string theory. It’s just too perfect, many think, to be mere coincidence.
Getting stuck on a brane: Brane worlds
With the introduction of all of these new objects, string theorists have begun exploring what they mean. One major step is the introduction of brane world scenarios, where our 3-dimensional universe is actually a 3-brane.
Ever since the inception of string theory, one of the major conceptual hurdles has been the addition of extra dimensions. These extra dimensions are required so the theory is consistent, but we certainly don’t seem to experience more than three space dimensions. The typical explanation has been to compactify the extra six dimensions into a tightly wound object roughly the size of the Planck length.
In the brane world scenarios, the reason we perceive only three spatial dimensions is that we live inside a 3-brane. There’s a fundamental difference between the space dimensions on the brane and those off the brane.
The brane world scenarios are a fascinating addition to the possibilities of string theory, in part because they may offer some ways in which we can have consistent string theories without resorting to elaborate compactification scenarios. Not everyone is convinced, however, that compactifications can be eliminated from the theory and even some brane world theories include compactification as well.
In the “Infinite dimensions: Randall-Sundrum models” section later in this topic, I look at some specific brane world scenarios that have been proposed, which offer some intriguing explanations for aspects of our universe, such as how to resolve the hierarchy problem (from topic 8). In topic 15, the idea of brane worlds allows you to consider the possibility of escaping our universe and traveling to a different universe on another brane!
