Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for the Born-Infeld and Dp-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite series in the auxiliary metric given by M. Abou Zeid and C.M. Hull, Phys. Lett. B 428 (1998) 277], but just picks out the first term from the series formally. New effective interactions of the theories are revealed.That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinitely many terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a (p-1)-form field strength. This non-linearity is inevitable under the requirement that the two dual actions are equivalent.