Ghost-free resummation of gravitational interactions of a 2-form gauge field

TL;DR

This paper demonstrates that a ghost-free interaction model for a 2-form gauge field in four dimensions can be viewed as a resummation of ghostly terms, with higher derivatives removable through specific equations, a property unique to four dimensions.

Contribution

It reveals the resummation structure of ghost-free interactions for 2-form gauge fields and analyzes their higher derivative properties in four dimensions.

Findings

Higher derivative terms can be eliminated by Euler-Lagrange equations.

Truncating at finite order breaks the ghost-free structure.

The ghost-free nature is specific to four-dimensional spacetime.

Abstract

We find that the recently-proposed ghost-free interaction of a 2-form gauge field in four dimensions, which contains derivative couplings in a nonperturbative manner, can be regarded as a resummation of ghostly interaction terms. We investigate the higher derivative structure of this model in a minisuperspace description and demonstrate that the higher derivative terms can be removed by taking appropriate combinations of the Euler-Lagrange equations, while a truncation at a finite order spoils this structure. We also show that this nature is peculiar to four dimensions.