SU(N) builder
Build a supported five-dimensional SU(N) model on S¹/Z₂ from boundary blocks and bulk matter, then inspect its one-loop potential and vacuum.
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 the builder as the starting point for a connected model investigation. The four blocks specify simultaneously diagonal boundary parities. Their sizes determine N and the apparent boundary-symmetry structure. The bulk fields supply the matter contributions to the potential. Neighbouring tools share this builder state, so you can inspect the spectrum and anomaly obligations without retyping the model.
First steps
- Start from a preset or enter the four nonnegative boundary-block sizes.
- Add supported bulk representations, their parity-product signs and copy counts.
- Read the resulting group and number of Wilson phases before interpreting the potential.
- Follow the same model into 4D spectrum, Anomalies, Brane matter and Simulator.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| n₊₊, n₊₋, n₋₊, n₋₋ | Nonnegative dimensions of the four simultaneous parity blocks. Their sum fixes the SU(N) rank parameter. | Load a preset first and identify which blocks are nonzero. |
| Bulk representation, ηη′ and multiplicity | Choose a supported field contribution, its boundary-sign product and the number of copies. | Add one supported copy while keeping the boundary blocks fixed. |
| Presets and clear bulk | Provide named starting inputs or a gauge-only matter setting. | Read a preset's boundary blocks before changing it. |
| Potential probe | Selects a phase at which to inspect the potential; the probe and the located vacuum are distinct positions. | Click away from the minimum and compare the probe information with the vacuum result. |
Reading the results
| Result | Meaning |
|---|---|
| Apparent unbroken subgroup | The group visible in the chosen boundary frame. Its appearance need not be invariant under gauge-equivalent boundary descriptions. |
| Potential terms and Wilson phases | Show what the supported matter and boundary data contribute and how many independent phase directions are being investigated. |
| Vacuum result | A located minimum or a stated undecided/unsupported result under the numerical method's scope. |
The builder covers the implemented boundary and representation families. A one-phase reduction permits additional moment diagnostics under their stated assumptions. A located vacuum may be undecided in a harder search; an unfinished calculation is not a proof that no vacuum exists.
Worked example
Carry one model through the laboratory
- Load a named builder preset.
- Record its blocks and bulk content.
- Open 4D spectrum and read its zero modes at the selected phase.
- Open Anomalies, then Brane matter if a completion is needed.
- Use Simulator for the model's dimensionful comparison.
What to expect: The same builder input is inspected from several perspectives. A favourable result in one view does not substitute for the others.
Formulas and conventions
N = n₊₊ + n₊₋ + n₋₊ + n₋₋
The boundary block dimensions add to the defining-representation dimension of SU(N).
Scope and limitations
- Supported representations and simultaneously diagonal parity blocks define the implemented model family; the builder does not represent every possible 5D theory.
- A brane interaction or supersymmetric cancellation absent from the implemented potential cannot be inferred from the model name.
- Minimum searches, moment approximations and global certificates have different scopes.
If something is unclear
There is no Wilson-line direction.
Inspect the chosen boundary blocks and surviving gauge-field components; a valid boundary condition need not leave a Higgs candidate.
The vacuum is labelled undecided.
Retain that status and inspect the stated search limitation. Do not substitute a symmetric point as a certified minimum.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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