On the boundedness of effective potentials arising from string compactifications

TL;DR

This paper proves that effective potentials from string theory compactifications are generally bounded from below, supporting a conjecture and providing conditions for critical points, with implications for string theory stability.

Contribution

It establishes the boundedness of effective potentials in string compactifications and offers criteria for the existence of critical points, advancing understanding of string theory stability.

Findings

Effective potentials are bounded from below under mild assumptions.

Sufficient conditions for the existence of critical points are derived.

The results support the conjecture on potential boundedness in string theory.

Abstract

We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative answer to a conjecture proposed by the second author in arXiv:0911.3378v4 [hep-th]. We also derive some sufficient conditions for the existence of critical points. All proofs and mathematical hypotheses are discussed in the context of their relevance to the physics of the problem.