GAUGE-INVARIANT AND GAUGE-FIXED D-BRANE ACTIONS

The first part of this paper presents actions for Dirichlet p-branes e mbedded 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 dime nsions is realized as a global symmetry. In addition the theories have local symmetries consisting of general coordinate invariance of the w orld-volume, a local fermionic symmetry (called ''kappa''), and U(1) g auge 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 pr esents 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 l ambda is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with p < 9 can be obtained from the 10D one by dimensional r eduction. (C) 1997 Published by Elsevier Science B.V.