Computational complexity of the landscape I

TL;DR

This paper demonstrates that finding physically relevant vacua in string theory is computationally NP-hard, implying significant challenges in explicitly identifying such vacua despite potential theoretical evidence.

Contribution

It proves that the problem of finding string theory vacua matching data is NP complete, highlighting fundamental computational limitations.

Findings

NP hardness of vacuum-finding problems

NP completeness of the Bousso-Polchinski model

Implications for string theory and cosmology

Abstract

We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the Bousso-Polchinski model, the problem is NP complete. We discuss the issues this raises and the possibility that, even if we were to find compelling evidence that some vacuum of string theory describes our universe, we might never be able to find that vacuum explicitly. In a companion paper, we apply this point of view to the question of how early cosmology might select a vacuum.