On Dimensional Reduction and Kaluza-Klein Modes
Q: The mechanism that collapses from 9D to observable 4D is sketched but not dynamically derived, right? How are unwanted Kaluza-Klein modes suppressed without fine-tuning?
A: The dimensional reduction mechanism is dynamically derived in the section on the Lagrangian/Action/Dynamics. By setting higher dimensional influences to zero, the effective 4D dynamics come into focus. The stuff happening on higher dimensions really doesn't have to be suppressed because it's higher level gauge theory stuff, but if you're only interested in 3D mechanical dynamics, you don't "need it".
Unlike traditional Kaluza-Klein theories, this model does not rely on compactified extra dimensions with Fourier modes. The higher-dimensional structure encodes global consistency conditions that project coherent, lower-dimensional dynamics rather than producing a tower of KK excitations. Hence, no fine-tuned suppression mechanism is required—such modes do not arise in this formalism. Kaluza Klein modes aren't something that naturally happens in this theory so they don't need to be suppressed.
On the Metric and Unit Flux Normalization
Q: The paper starts without a metric, but normalising the Laplacian or defining “unit” flux seems to import one. Where does the metric choice come from?
A: This theory is fundamentally a topological picture to start with, so we start with the shape of the field itself and begin without a metric. The emergence of a pseudo-metric structure arises dynamically via the constraint structure of the BF-type action and from the embedding geometry of the lower-dimensional fibers. So we basically just take a look at an effective slice of S3, which is where 3D dynamics emerge, and there's the pseudo-metric. If you could explain the context for the "unit flux" that would help.
On Parameter-Free Predictions and Empirical Inputs
Q: If the overall scale is fixed by comparing one predicted constant to experiment, are the other predictions really parameter-free? How many empirical inputs does the theory need to calibrate its spectra?
A: The theory derives the Higgs vacuum expectation value (VEV) topologically from the structure of the bundle and its knot invariants fairly early on in the paper, so I don't rederive in the constants section. The constants are all derived relative to using topological and spectral properties (e.g., normalized Chern-Simons invariants, torsion, and interference eigenvalues). No additional empirical parameters are introduced or fit by hand.
