Constructing doubly self-dual chiral p-form actions in D=2(p+1) spacetime dimensions

A Siegel-type chiral p-form action is proposed in D = 2(p + 1) spacetime di mensions. The approach we adopt is to realize the symmetric second-rank Lag range-multiplier field, introduced in Siegel's action, in terms of a normal ized multiplication of two (q + 1)-form fields with q indices of each field contracted in the even p case, or of two pairs of (q + 1)-form fields with q indices of each pair of fields contracted in the odd p case, where the ( q + 1)-form fields are of external derivatives of one auxiliary q-form fiel d for the former, or of a pair of auxiliary q-form fields for the latter. U sing this action, it is straightforward to deduce the recently constructed PST action for q equal to zero. It is found that the Siegel-type chiral p-f orm action with a fixed p (even or odd) is doubly self-dual in D = 2(p + 1) spacetime dimensions when the auxiliary field(s) is/are also chosen to be of p-form. This result includes PST's as a special case where only the chir al 0-form action is doubly self-dual in D = 2 dimensions. (C) 2001 Elsevier Science B.V. All rights reserved.