Computational Complexity of Vacua and Near-Vacua in Field and String Theory

Abstract

We demonstrate that the problems of finding stable or metastable vacua in a low energy effective field theory requires solving nested NP-hard and co-NP-hard problems, while the problem of finding near-vacua is in P. Multiple problems relevant for computing effective potential contributions from string theory are shown to be instances of NP-hard problems. If P $\ne$ NP, the hardness of finding string vacua is exponential in the number of scalar fields. Cosmological implications, including for rolling solutions, are discussed in light of a recently proposed measure.

9 pages. PRD Version

References in corpus (13)

• De Sitter vs Quintessence in String Theory
• The dS swampland conjecture and the Higgs potential
• Computational complexity of the landscape I
• Machine Learning of Calabi-Yau Volumes
• Machine Learning in the String Landscape
• Cohomology of Line Bundles: A Computational Algorithm
• Evolving neural networks with genetic algorithms to study the String Landscape
• Heterotic MSSM on a Resolved Orbifold
• On Algorithmic Universality in F-theory Compactifications
• Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties
• The de Sitter swampland conjecture and supersymmetric AdS vacua
• Quantum Corrections and the de Sitter Swampland Conjecture
• Fast optimization algorithms and the cosmological constant

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