Gauge-invariant and gauge-fixed D-brane actions

The first part of this paper presents actions for Dirichlet p-branes embedded in a flat ten-dimensional space-time. The fields of the (p + 1)-dimensional world-volume theories are the 10D space-time coordinates X-m, a pair of Majorana-Weyl spinors theta(1) and theta(2), and a U(1) gauge field A(mu). The N = 2A or 2B super-Poincare group in ten dimensions is realized as a global symmetry. In addition the theories have local symmetries consisting of general coordinate invariance of the world-volume, a local fermionic symmetry (called ''kappa''), and U(1) gauge invariance. A detailed proof of the kappa symmetry is given that applies to all cases (p = 0, 1,...,9). The second part of the paper presents gauge-fixed versions of these theories. The fields of the 10D (p = 9) gauge-fixed theory are a single Majorana-Weyl spinor lambda and the U(1) gauge field A(mu). This theory, whose action turns out to be surprisingly simple, is a supersymmetric extension of 10D Born-Infeld theory. It has two global supersymmetries: one represents an unbroken symmetry, and the second corresponds to a broken symmetry for which lambda is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with p < 9 can be obtained from the 10D one by dimensional reduction. (C) 1997 Published by Elsevier Science B.V.