D-Brane: Superstrings and New Perspective of Our World
by Koji Hashimoto

Springer, 2012, 165 pages

Reviewed by T. Nelson

hat is a brane? Is it a field, a physical object, an energy excitation, or a unit of space?

In some sense it might be all of the above: many suspect that at the deepest level, there must only be one thing in the universe. But for the purposes of this book, a brane is a generalization of the concept of a string. A brane can have 0, 1, 2, up to 10 dimensions (plus one more for time). For a 1-dimensional string, which a conjecture called S-duality says is the same as a D1-brane, the way it vibrates determines what kind of particle it may be, such as electron, photon, or quark.

In another sense a brane is a mathematical construct. Whether it really looks like a piece of string is irrelevant; if it explains the real world, then it's useful. Theories are like hamburgers: the extra stuff around the outside has no nutritive value, but is there to help us hold on to the beef inside, so we can ask interesting questions. In this case, we want to know where the four forces of nature come from, why there are four dimensions, and why particles have the masses that we observe. Physicists can also use the math to describe the behavior of matter at extremes, such as in a black hole or at the Big Bang, that can't be modeled by our current theories.

D-Brane fills an important gap between the light pop-science books and textbooks like Strings and Branes by Peter West, Becker's String Theory and M-Theory, Zwiebach's A First Course in String Theory, and the two-volume, 976-page book by Polchinski, the guy who invented D-branes. Unlike these, to read D-Brane you only need undergraduate physics, and no understanding of quantum mechanics or relativity.

That doesn't mean you won't learn a lot. It's a fascinating book, but I found that I knew less about branes after finishing it than when I started. That's a roundabout way of saying the theory raises more questions than it answers.

For example, Hashimoto says the Big Bang might have occurred when a D-brane and an anti-D-brane touched. This doesn't mean they annihilated each other, because the branes reconnect in much the same way that magnetic lines of force reconnect on the Sun. Did this create the material for the Big Bang? And if the direction of a string represents its electric charge, but a string is infinitely long, isn't the charge per unit length zero?

Ah, says Hashimoto, but space is curved in string theory, and therefore the strings aren't really infinitely long. By curved he means, of course, compactified to atomic or even Planck dimensions, which means these infinite strings are actually quite short. Compactifi­cation gives them new properties that string theorists hope can be pounded into something that matches the real world.

There's also a good description of anti-deSitter space and the AdS/CFT conjecture, which is the most exciting thing from string theory so far. And of course tachyons, which are real again, and gravity, which is what strings were invented to explain.

Hashimoto says D-branes are solitons, which are waves that travel long distances without losing energy, like a wave in a boat canal. They are also black holes, he says, or more properly charged black branes. This seems not to be a universal interpretation, although there is such a thing as brane cosmology, which hypothesizes that the universe is on a gigantic brane. Some scientists have modeled black holes as collections of large numbers of branes (see here and here), but also there is a correspondence between black holes and D-branes at the low-energy limit.

These conflicting descriptions are meant to convince us that branes are real, and to demonstrate their potential power, but they left me confused. Aren't branes really just Planck scale phenomena? How could they be black holes, which are really big?

Details. It seems that string theorists find it easier to discuss infinite branes first, and worry about compactification later; Hashimoto talks about the ‘internal space’ in which D-branes interact, and says it actually ‘should be compactified to be small.’

Hashimoto's primary language is clearly not English, and he's obviously trying to simplify things. Despite this, this little book is dense with insights. Anyone starting out would benefit from reading it a couple of times.

String theory is not a complete theory yet, let alone a theory of everything. The jury is still out on which parts are the beef and which are the sesame seed bun.

jun 17, 2017