Constructing Doubly Self-Dual Chiral p-Form Actions in D=2(p+1) Spacetime Dimensions

TL;DR

This paper introduces a new Siegel-type chiral p-form action in D=2(p+1) dimensions, demonstrating its doubly self-dual property when auxiliary fields are p-forms, unifying and extending previous formulations like PST.

Contribution

It constructs a novel Siegel-type action for chiral p-forms that achieves double self-duality in D=2(p+1) dimensions, generalizing existing models.

Findings

The action is doubly self-dual with p-form auxiliary fields.

Special case reduces to PST's chiral 0-form action.

Unifies chiral p-form actions in a symmetric framework.

Abstract

A Siegel-type chiral p-form action is proposed in D=2(p+1) spacetime dimensions. The approach we adopt is to realize the symmetric second-rank Lagrange-multiplier field, introduced in Siegel's action, in terms of a normalized 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 field for the former, or a pair of auxiliary q-form fields for the latter. Using 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-form 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 chiral 0-form action is doubly self-dual in D=2 dimensions.