This research proposes a methodological framework to construct continuous spectral triples for quantum field theory applications, combining noncommutative geometry with conformal bootstrap methods. The approach introduces a spectral bootstrap procedure to iteratively construct compatible spectral data while preserving essential analytic properties.
Key findings
Develops a spectral bootstrap algorithm for continuous spectral triples.
Establishes regularization schemes mapping continuous spectral densities to discrete approximations.
Validates the method through numerical experiments in two-dimensional CFTs and the Standard Model.
Demonstrates predictive power for strongly coupled gauge theories.
Limitations & open questions
Further validation needed for broader QFT applications
Complexity of solving Dirac operator in interacting QFTs