Noether Currents and Maxwell-type Equations of Motion in Higher Derivative Gravity Theories

TL;DR

This paper constructs Noether currents in higher derivative gravity theories and demonstrates that their equations of motion can be expressed as Maxwell-type equations with these currents as sources.

Contribution

It introduces a method to derive Maxwell-type equations of motion from Noether currents in complex higher derivative gravity theories.

Findings

Noether currents are explicitly constructed for these theories.

Equations of motion can be reformulated as Maxwell-type equations.

The Noether currents serve as source terms in these equations.

Abstract

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi's IOSp(8|8) choral symmetry containing the BRS symmetry as its member, are constructed. We generally show that for each of those Noether currents a suitable linear combination of equations of motion can be brought into the form of Maxwell-type field equation possessing the Noether current as its source term.