Towards Higher-n Superextensions of Born-infeld Theory

The main source of current interest in superextensions of the Born-Infeld (or Dirac-Born-Infeld) action is the fact that these super BI actions constitute an essential part of the worldvolume actions of Dp-branes (see [1] and refs. therein). It is tempting to formulate super BI actions in a manifestly supersymmetric way using an off-shell superfield approach. In this approach the worldvolume SUSY is linearly realized, as opposed to the approach proceeding from a gauge-fixed form of the Green-Schwarz Dp-actions [2], in which all SUSYs are nonlinear and non-manifest. As was shown in [3], the N = 1, d = 4 super BI theory first formulated in [4] in terms of superfields can be re-interpreted as a theory of partial spontaneous breaking of global N = 2 SUSY (PBGS) down to N = 1 SUSY, with vector N = 1 multiplet as the relevant Goldstone multiplet. Thus the PBGS approach provides a powerful way of deriving super BI actions with extra hidden nonlinearly realized supersymmetries. This contribution is a brief survey of super BI theories of this kind known to date. A short description of the recently constructed N = 3 supersymmetric BI theory [5] is also given.