Higher derivative three-form gauge theories and their supersymmetric extension

TL;DR

This paper explores higher derivative three-form gauge theories and their supersymmetric extensions, identifying conditions for ghost and tachyon freedom, and establishing consistent boundary terms in four-dimensional spacetime.

Contribution

It demonstrates that ghost and tachyon-free higher derivative interactions can be constructed for three-form gauge theories and their supersymmetric extensions, with explicit boundary terms.

Findings

Higher derivative terms with quadratic kinetic form produce tachyons or ghosts.

Functions of the field strength avoid ghosts and tachyons.

Boundary terms are essential for consistent equations of motion and energy-momentum tensors.

Abstract

We investigate three-form gauge theories with higher derivative interactions and their supersymmetric extensions in four space-time dimensions. For the bosonic three-form gauge theories, we show that derivatives on the field strength of the 3-form gauge field yield a tachyon as far as the Lagrangian contains a quadratic kinetic term, while such the term with opposite sign gives rise to a ghost. We confirm that there is neither a tachyon nor a ghost when all higher derivative terms are given by functions of the field strength. For this ghost/tachyon-free Lagrangian, we determine the boundary term necessary for the consistency between the equation of motion and energy-momentum tensor. For supersymmetric extensions, we present ghost/tachyon-free higher derivative interactions of arbitrary order of the field strength and corresponding boundary terms as well.