D-Branes , Clifford V. Johnson , Cambridge U. Press, New York 2003. $60.00 (548 pp.). ISBN 0-521-80912-6
In the mid-1990s, theorists realized that string theory contained other objects in addition to strings. Those extended “p-branes” appeared as solutions to the theory in the classical limit of vanishing Planck’s constant. P-branes can have various dimensionalities. A 0-brane has zero spatial dimensions, so it is a point particle. A 1-brane has one spatial dimension like a string. A 3-brane, with its three extended spatial dimensions, could be like the world we live in. Dirichlet-branes, or D-branes for short, are p-branes on which open strings can end. The name arises because the strings may be said to have Dirichlet boundary conditions at their endpoints.
As Joseph Polchinski showed in a seminal 1995 paper published in Physical Review Letters, D-branes can be described in a simple and precise mathematical fashion. That understanding has led to a plethora of interesting and important results. Among the most notable are the explanation of the microscopic origin of black hole entropy; string dualities relating strong and weak coupling; the connection between gravity on certain negatively curved spacetimes called anti–de Sitter (AdS) spaces and “conformal” field theories (CFTs) that are reminiscent of quantum chromodynamics; and the realization that we might live on a 3-brane that is part of a larger space with millimeter-sized extra dimensions.
Clifford Johnson’s D-Branes presents the basic mathematical technology necessary for dealing with this subject. It also nicely describes many of the important results that D-branes have led to. The author starts with an overview of string theory and then describes D-brane properties. He systematically introduces many topics that provide insight about D-branes. Examples include the study of anomalies in theories whose fields live on the world volume of D-branes propagating through spacetime, supergravity solutions associated with D-branes, bound states of D-branes, and D-branes as probes of geometry at length scales smaller than the string length. One chapter, which details the connection between D-branes and black holes, clearly explains how one can compute the microscopic origin of black hole entropy. That first-principles entropy calculation was one of the landmark achievements of string theory as a theory of quantum gravity, and a thorough understanding of the physics of D-branes is necessary for deriving it. In a couple of chapters that consider the AdS-CFT correspondence, Johnson puts special emphasis on comparing the thermodynamics of the theories.
D-branes have led to new approaches to “compactifying” string theory so that only the four familiar spacetime dimensions are large. They have inspired new ways to think about the origin of gauge symmetry. Because D-branes naturally have gauge fields defined on their world volumes, they suggest that matter could be localized on a 3-brane that lives in a higher-dimensional space. Johnson details various simple supersymmetric models realizing that suggestion.
Johnson has first-hand experience with the material he discusses and has made important contributions to many of the topics described in his book. Together with Polchinski and Shyamoli Chaudhuri, he wrote the first review on D-branes (1996), which was based on lectures delivered by Polchinski. Johnson’s book is more extensive and grew out of material he presented in various courses and summer schools.
D-Branes is an excellent complement to other existing texts on string theory, such as the two-volume Superstring Theory (Cambridge U. Press, 1987) by Michael Green, John Schwarz, and Edward Witten or Polchinski’s two-volume String Theory (Cambridge U. Press, 1998), which has a chapter devoted to D-branes. Johnson’s book has a clear and direct presentation, and contains nice clarifying inserts explaining various bits of commonly used mathematics. I expect it will be a valuable tool for graduate students who intend to work in string theory and also a useful reference for active researchers.
