String/M-branes for Relativists

Abstract

These notes present an introduction to branes in ten and eleven dimensional supergravity and string/M-theory which is geared to an audience of traditional relativists, especially graduate students and others with little background in supergravity. They are designed as a tutorial and not as a thorough review of the subject; as a result, many topics of current interest are not addressed. However, a guide to further reading is included. The presentation begins with eleven dimensional supergravity, stressing its relation to 3+1 Einstein-Maxwell theory. The notion of Kaluza-Klein compactification is then introduced, and is used to relate the eleven dimensional discussion to supergravity in 9+1 dimensions and to string theory. The focus is on type IIA supergravity, but the type IIB theory is also addressed, as is the T-duality symmetry that relates them. Branes in both 10+1 and 9+1 dimensions are included. Finally, although the details are not discussed, a few comments are provided on the relation between supergravity and string perturbation theory and on black hole entropy. The goal is to provide traditional relativists with a kernel of knowledge from which to grow their understanding of branes and strings.