Computational complexity of the landscape I

TL;DR

The paper investigates the computational complexity of finding string theory vacua that match observed data, showing that the problem is typically NP-hard and that the BP model is NP-complete. It connects these results to a broader set of lattice problems and complexity classes, highlighting the physical implications of intractable search in high-dimensional landscapes, such as metastability and exponential relaxation. The authors argue that even if a suitable vacuum exists, explicit identification may be infeasible, and that measure factors and anthropic considerations can intensify the difficulty, guiding researchers toward statistical and probabilistic approaches. The work discusses practical consequences for testing string theory and suggests that a full, explicit catalog of vacua may be beyond reach, while still enabling meaningful scientific inferences and predictions, with a companion paper extending these ideas to early-universe dynamics.

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.