Relating Hodge Atoms, Spectral Triples, and BPS Flows

TL;DR

This paper explores the connections between algebraic and analytic frameworks in birational invariants, focusing on non-commutative Hodge structures and their implications for quiver gauge theories on cubic fourfolds, proposing a conjecture about quantum phases.

Contribution

It introduces a novel perspective linking non-commutative Hodge structures with quantum phases in gauge theories, and proposes a conjecture about the invariance of spectra under tunneling.

Findings

Interpretation of semiorthogonal property as a dynamical selection rule

Proposal that the K3 Hodge atom corresponds to a protected quantum phase

Conjecture on spectral invariance under non-perturbative tunneling

Abstract

We compare algebraic and analytic pictures relevant to the study of birational invariants. Motivated by recent advances in the development of non-commutative Hodge structures, we examine their implication for quiver gauge field theory on the cubic fourfold. By interpreting the semiorthogonal property as a dynamical selection rule, we conjecture that the K3 Hodge atom of the cubic fourfold represents a protected quantum phase whose spectra remain invariant under non-perturbative tunneling processes.