Unitarity analysis of general Born-Infeld gravity theories

TL;DR

This paper develops methods to analyze the unitarity of general Born-Infeld gravity theories in arbitrary dimensions, simplifying the process by focusing on key curvature terms and applying the approach to four-dimensional cases.

Contribution

The authors introduce a compact technique to assess unitarity of BI gravity actions, reducing complexity by identifying finite curvature terms relevant in even dimensions.

Findings

Unitarity depends only on finite curvature terms in even dimensions.

The developed methods simplify unitarity analysis of complex BI gravity actions.

Application to 4D examples demonstrates the effectiveness of the approach.

Abstract

We develop techniques of analyzing the unitarity of general Born-Infeld (BI) gravity actions in D-dimensional spacetimes. Determinantal form of the action allows us to find a compact expression quadratic in the metric fluctuations around constant curvature backgrounds. This is highly nontrivial since for the BI actions, in principle, infinitely many terms in the curvature expansion should contribute to the quadratic action in the metric fluctuations around constant curvature backgrounds, which would render the unitarity analysis intractable. Moreover in even dimensions, unitarity of the theory depends only on finite number of terms built from the powers of the curvature tensor. We apply our techniques to some four-dimensional examples.