The inheritance of energy conditions: Revisiting no-go theorems in string compactifications

TL;DR

This paper examines how energy conditions in string theory constrain possible four-dimensional cosmological backgrounds, revealing conditions under which these backgrounds can or cannot violate these energy constraints.

Contribution

It classifies how higher-dimensional energy conditions influence lower-dimensional solutions in string compactifications, clarifying assumptions behind no-go theorems.

Findings

Energy conditions are generally satisfied in supergravity actions.

Objects violating energy conditions individually are compatible with tadpole cancellation.

Conditions are identified under which higher-dimensional energy conditions imply lower-dimensional ones.

Abstract

One of the fundamental challenges in string theory is to derive realistic four-dimensional cosmological backgrounds from it despite strict consistency conditions that constrain its possible low-energy backgrounds. In this work, we focus on energy conditions as covariant and background-independent consistency requirements in order to classify possible backgrounds coming from low-energy string theory in two steps. Firstly, we show how supergravity actions obey many relevant energy conditions under some reasonable assumptions. Remarkably, we find that the energy conditions are satisfied even in the presence of objects which individually violate them due to the tadpole cancellation condition. Thereafter, we list a set of conditions for a higher-dimensional energy condition to imply the corresponding lower-dimensional one, thereby categorizing the allowed low-energy solutions. As for any no-go theorem, our aim is to highlight the assumptions that must be circumvented for deriving four-dimensional spacetimes that necessarily violate these energy conditions, with emphasis on cosmological backgrounds.