Maxwell $F^N$ Characteristic Equation Algorithm Applied to Abelian Born-Infeld Action in Dp-branes

TL;DR

This paper introduces an algorithm to generate Maxwell field strength invariant identities, simplifying the Abelian Born-Infeld action across multiple dimensions relevant to Dp-branes.

Contribution

The paper presents a novel algorithm for deriving characteristic identities among Maxwell invariants, aiding in the simplification of the Abelian Born-Infeld action in various dimensions.

Findings

Derived simplified Abelian Born-Infeld actions in 4, 6, 8, 10, and 12 dimensions.

Established linear dependence relations among Maxwell invariants in specific dimensions.

Provided explicit formulas for Dp-brane effective actions.

Abstract

An algorithm is devised to generate characteristic identities between Maxwell fieldstrength invariants (traced over Lorentz indices and disregarding ordering) that suffer linear dependence in certain dimensionalities as they have been originally obtained using a Maple routine. These relations between invariants are then applied to simplify the Abelian Born-Infeld (ABI) effective action in arbitrary degree of fieldstrength invariants. I have explicitly displayed the simplified ABI action in 4, 6, 8, 10, and 12 space-time dimensions relevant in Dp-branes.