4D spectrum
What the model on the builder CONTAINS: the four-dimensional fields and their Kaluza–Klein towers.
Control names are kept as they appear in the application. Start with a reference, change one input at a time, and retain the assumptions with your result.
What this tool is for
Use this to identify the four-dimensional fields supplied by the builder model and how their higher Kaluza–Klein levels are organized. The tables distinguish a family description useful for the potential from the exact tower accounting needed at exceptional low levels.
First steps
- Edit the model in SU(N) builder — this section shares it.
- Choose at the vacuum or type a phase.
- Read the massless content, then the families, then the exact tower and its landscape.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Shared builder model | Determines the boundary blocks and bulk representations whose spectrum is displayed. | Use the named SU(6) example, then inspect the same blocks in the builder. |
| At the vacuum / phase probe | Chooses whether to evaluate the spectrum at the located vacuum or at a manually selected phase. | Compare a symmetric point with the available broken vacuum. |
| Spectrum landscape | A rotatable view of the calculated levels; the tables retain the detailed multiplicities and labels. | Read the lowest levels in the exact table before relying on the picture. |
Reading the results
| Result | Meaning |
|---|---|
| Massless content and chirality | The surviving four-dimensional components under the selected boundary and phase conditions. |
| Tower families | A compact organization of spectral contributions useful for reconstructing the potential. |
| Exact low-level tower | Resolves low-level details that the potential-family multiset alone does not describe correctly for every representation at a broken vacuum. |
The families are the potential's multiset and are right for it; at a broken vacuum they are wrong at the LOWEST level of the adjoint and the symmetric tensor, which is why the exact tower is a second table and not a repetition.
Worked example
Compare the symmetric point with the vacuum
- Load the supplied SU(6) example.
- Inspect the massless content at the symmetric point.
- Switch to the located vacuum if available.
- Compare the lowest exact levels, multiplicities and chirality labels.
What to expect: A phase change can alter which states remain massless. The potential's term multiplicities are not a substitute for the exact lowest-level spectrum.
Scope and limitations
- The spectrum uses the supported builder model and its boundary conditions.
- Additional boundary masses and interactions require the separate completion analysis.
- A plotted tower does not establish experimental production or decay rates.
If something is unclear
The family and exact tables appear to disagree at the lowest level.
Read the page's explanation of exceptional lowest modes, especially for adjoint and symmetric-tensor fields at a broken vacuum.
At the vacuum is unavailable.
Return to the builder and inspect whether a vacuum was located or left undecided.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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