Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions

TL;DR

This paper generalizes the concept of Hodge-type duality and self-duality for p-form fields across arbitrary dimensions, introducing a new framework that extends traditional restrictions and connects to known models like Maxwell theory.

Contribution

It introduces a novel, well-defined notion of self-duality for tensorial doublets in any dimension, expanding the scope of duality symmetry beyond even-dimensional spacetimes.

Findings

Defines a generalized self-dual action valid in arbitrary dimensions.

Constructs a master-action interpolating various models.

Finds semi-self-duality as a parent action for Maxwell-type theories.

Abstract

It is often claimed [PST1] that the (Hodge type) duality operation is defined only in even dimensional spacetimes and that self-duality is further restricted to twice-odd dimensional spacetime theories. The purpose of this paper is to extend the notion of both duality symmetry as well as self-duality. By considering tensorial doublets, we introduce a novel well-defined notion of self-duality based on a duality Hodge-type operation in arbitrary dimension and for any rank of these tensors. Thus, a generalized Self-Dual Action is defined such that equations of motion are the claimed generalized self-duality relations. We observe in addition, that taking the proper limit on the parameters of this action, it always provides us with a master-action, which interpolates models well-studied in physics; by considering a particular limit, we find an action which describes an interesting type of relation, referred to as semi-self-duality, which results to be the parent action between Maxwell- type actions. Finally, we apply these ideas to construct manifest Hodge-type self-dual solutions in a (2+1)-dimensional version of the Maxwell's theory.