Five dimensions
Evaluate the supported Haba–Yamashita five-dimensional SU(3) example and compare its potential, located vacuum and Kaluza–Klein spectrum.
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 compact example to learn how matter and boundary signs shape a Wilson-line potential. The six counts separate the supported adjoint fermion, fundamental fermion and scalar contributions by parity-product sign. The preset buttons supply controlled comparisons without requiring a new model from scratch.
First steps
- Load the archived row, then identify the six matter counts and their parity-product signs.
- Compare the evaluated potential with its located minimum and the separate approximation when available.
- Use the pure-gauge, marginal-trio and blind-step examples to change one structural feature at a time.
- Read the spectrum at the resulting phase and retain this model's normalization conventions.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Adjoint fermion counts, + and − | Numbers of the supported adjoint Dirac fields in the two parity-product sectors. | Start from the archived row and change one count. |
| Fundamental fermion and scalar counts, + and − | Separate fermionic and complex-scalar contributions; their signs and degrees of freedom enter the potential differently. | Use the blind-step button to inspect the specific cancelling combination. |
| Archived row / pure gauge / marginal trio | Load the named reference or a targeted example with stated matter content. | Compare pure gauge with the marginal trio while reading the potential and moment diagnostics. |
Reading the results
| Result | Meaning |
|---|---|
| Evaluated potential and minimum | The phase dependence of the implemented source formula and the minimum located for that input. |
| Moment/rung diagnostics | Describe the arithmetic of this supported five-dimensional content, including its even-rung property. |
| KK spectrum | The tower structure at the selected vacuum under this model's boundary and normalization conventions. |
This is a particular 5D model family. Its even-rung arithmetic and phase normalization should not be replaced by those of the 6D SU(7) family. The located vacuum and a small-angle approximation must be compared within their domains.
Worked example
Separate a content change from a potential change
- Load the archived row and note its potential.
- Apply the blind-step example.
- Check the changed counts and compare the potential.
- Use the marginal-trio example and inspect the changed vacuum behaviour.
What to expect: Different matter counts can have the same implemented potential contribution. The preset states which combination is being tested.
Scope and limitations
- The page covers the stated SU(3) family and supported matter sectors.
- The 5D parity-product and phase conventions differ from those of the SU(7) family.
- A one-loop vacuum and spectrum do not establish a complete phenomenological model.
If something is unclear
A content change leaves the curve unchanged.
Check whether the change is the displayed blind combination of fermion and scalar contributions.
The approximation is unavailable near a marginal case.
Read the direct potential and the stated domain restriction instead of forcing a small-angle formula.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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