# Duality invariant self-interactions of abelian p-forms in arbitrary dimensions

## TL;DR

This paper develops a universal algebraic method to construct non-linear, duality-invariant Maxwell theories in arbitrary dimensions, generalizing known models and deriving new interactions, with implications for theories involving charged p-branes.

## Contribution

It introduces a universal algebraic approach to build non-linear duality-invariant Maxwell theories in any dimension, extending previous models and deriving new interactions, especially in D=8.

## Key findings

- Derived a general consistency condition for duality and Lorentz invariance.
- Constructed new non-canonical duality-invariant quartic interactions in D=8.
- Established the equivalence and physical differences between PST and GZGR formulations.

## Abstract

We analyze non-linear interactions of 2N-form Maxwell fields in a space-time of dimension D=4N. Based on the Pasti-Sorokin-Tonin (PST) method, we derive the general consistency condition for the dynamics to respect both manifest SO(2)-duality invariance and manifest Lorentz invariance. For a generic dimension D=4N, we determine a canonical class of exact solutions of this condition, which represent a generalization of the known non-linear duality invariant Maxwell theories in D=4. The resulting theories are shown to be equivalent to a corresponding class of canonical theories formulated a la Gaillard-Zumino-Gibbons-Rasheed (GZGR), where duality is a symmetry only of the equations of motion. In dimension D=8, via a complete solution of the PST consistency condition, we derive new non-canonical manifestly duality invariant quartic interactions. Correspondingly, we construct new non-trivial quartic interactions also in the GZGR approach, and establish their equivalence with the former. In the presence of charged dyonic p-brane sources, we reveal a basic physical inequivalence of the two approaches. The power of our method resides in its universal character, reducing the construction of non-linear duality invariant Maxwell theories to a purely algebraic problem.