Turing's Landscape: decidability, computability and complexity in string theory

TL;DR

This paper explores how concepts of decidability and computability influence the understanding of string theory's Landscape, highlighting the widespread presence of undecidability in fundamental aspects of string vacua.

Contribution

It emphasizes the importance of algorithmic questions in string theory and demonstrates the pervasiveness of undecidability beyond previous studies.

Findings

Average gauge group rank in the Landscape is linked to undecidability.

Constructing Ricci-flat metrics on Calabi-Yau manifolds involves undecidable problems.

Computability of fundamental periods in string theory is often undecidable.

Abstract

I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the average rank of the (unification) gauge group in the Landscape, the explicit construction of Ricci-flat metrics on Calabi-Yau manifolds as well as the computability of fundamental periods to show that undecidability questions are far more pervasive than that described in the work of Denef and Douglas.