Formalizing the stability of the two Higgs doublet model potential into Lean: identifying an error in the literature

TL;DR

This paper formalizes the 2006 stability analysis of the two Higgs doublet model potential using Lean, uncovering a significant error that invalidates the main theorem and highlighting the value of formal verification in physics.

Contribution

It demonstrates how formalization in Lean can identify errors in existing physics literature, specifically correcting a key result in the 2HDM potential stability proof.

Findings

An error in the 2006 paper's proof was discovered through formalization.

The main theorem on 2HDM potential stability was invalidated.

First known case of a physics paper error found via formal proof assistant.

Abstract

In 2006, using the best methods and techniques available at the time, Maniatis, von Manteuffel, Nachtmann and Nagel published a now widely cited paper on the stability of the two Higgs doublet model (2HDM) potential. Twenty years on, it is now easier to apply the process of formalization into an interactive theorem prover to this work thanks to projects like Mathlib and Physlib (the latter formerly PhysLean and Lean-QuantumInfo), and to ask for a higher standard of mathematical correctness. Doing so has revealed an error in the arguments of this 2006 paper, invalidating their main theorem on the stability of the 2HDM potential. This case is noteworthy because to the best of our knowledge it is the first non-trivial error in a physics paper found through formalization. It was one of the first papers where formalization was attempted, which raises the uncomfortable question of how many physics papers would not pass this higher level of scrutiny.