Brane matter
Who pays that bill, and what it costs: matter on the two fixed points, held at once to the anomaly ledger and to Part I's boundary-mass gate.
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 add explicit matter at the two orbifold endpoints and inspect two consequences: changes to the anomaly ledger and possible boundary masses for unwanted zero modes. The local groups at the two endpoints can differ, so a representation that is available at one boundary need not be available at the other.
First steps
- Edit the model in SU(N) builder — or press the example to load Kawamura's SU(5).
- Read the two branes first: they are different groups whenever the orbifold breaks anything.
- Add fields with the + buttons, or pick a massless mode and let the partners panel say which representations contain its conjugate.
- Press solve to get the local charges that cancel the linear channels.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Builder model / Kawamura SU(5) example | Sets the bulk model and its local boundary groups. | Load the named example and read both boundary-group headings. |
| Boundary fields and copy counts | Add representations of the selected endpoint's local group. | Use the partner suggestions for one massless mode before adding fields arbitrarily. |
| Boundary charges and linear-channel solver | Choose charges or solve the stated linear anomaly conditions. The remaining channels still need inspection. | Compare the suggested charge with the charge required for a boundary mass. |
| Clear / reset charges / return to builder model | Restore a defined starting point for a controlled comparison. | Save the current choices before resetting. |
Reading the results
| Result | Meaning |
|---|---|
| Anomaly ledger before and after | Shows what the added fields contribute in the same channel conventions. |
| Possible partners | Lists supported local representations that contain a conjugate partner for the selected mode. |
| Surviving massless content | The rank-based result assumes generic allowed couplings; the displayed surviving count is a lower bound under that assumption. |
Two verdicts, kept apart on purpose: the bill before and after, and the massless count before and after. The same field can pay one and not the other, because the charge that cancels an anomaly is not in general the charge a mass term needs. The surviving count is a lower bound — the rank test assumes generic couplings.
Worked example
Check the cost of removing a zero mode
- Load Kawamura's SU(5) example.
- Choose an unwanted massless mode and inspect its possible partners.
- Add a suggested local representation.
- Compare both the anomaly ledger and the boundary-mass condition, including its charge.
What to expect: A field that helps one requirement can leave another unresolved. Read the two outcomes independently.
Scope and limitations
- Solving the linear anomaly channels does not by itself solve every cubic condition.
- Generic-coupling rank information does not specify actual numerical masses or a complete Yukawa sector.
- Only the supported local representations and boundary-mass conditions are examined.
If something is unclear
The anomaly-solving charge does not permit the desired mass term.
Keep both conditions explicit and try another supported completion; do not treat the two charge requirements as interchangeable.
A representation introduces additional fields.
Read its full local decomposition, then include those fields in the updated ledger and surviving-content count.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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