GEOMETRIC ACTIONS FOR D-BRANES AND M-BRANES

New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fie lds couple both to a background or induced metric and a new auxiliary metric, whose elimination reproduces the non-polynomial Born-Infeld ac tion. This is similar to the introduction of an auxiliary metric to si mplify the Nambu-Goto string action. This simplifies the quantisation and dualisation of the gauge fields. (C) 1998 Elsevier Science B.V. Al l rights reserved.