Anomalies
What that content owes: every anomaly channel of the unbroken group, in exact rationals.
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 after inspecting the builder spectrum. It sums the supported chiral massless content into the anomaly channels of the displayed unbroken group. Exact rational arithmetic makes a cancellation distinguishable from a small floating-point residual.
First steps
- Edit the model in SU(N) builder.
- Read the channels: [SU(n)]³, U(1)×[SU(n)]², U(1)³, U(1)×[grav]².
- Read the verdict: no subject, cancels, or owes.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Shared builder content | Supplies the boundary conditions and matter being checked. | Load the supplied SU(6) example and inspect its massless fermions before reading the ledger. |
| Model and spectrum choices | Determine which supported chiral fields are included in the stated ledger. | Change one builder field, then compare the summands as well as the total. |
Reading the results
| Result | Meaning |
|---|---|
| SU(n)³ and mixed U(1) channels | Separate non-Abelian, mixed, Abelian and mixed gravitational anomaly combinations under the displayed normalization. |
| Summand table | Names the chiral fields contributing to each channel; it explains the total. |
| No subject / cancels / owes | Distinguishes absence of relevant massless fermions, cancellation of the stated ledger, and a nonzero contribution requiring a completion. |
A non-zero row is a BILL, not an inconsistency: the brane fermions such a model needs pay into the same channels with the opposite sign. And a model with no massless fermion has nothing to cancel — that is `no subject`, not `cancels`.
Worked example
Read a cancellation claim from its ingredients
- Load the supplied example.
- Check the list of massless chiral fermions.
- Read every nonzero channel and its contributors.
- Open Brane matter to inspect a possible completion.
What to expect: A zero obtained from an empty fermion list is identified separately from cancellation between nonzero contributions.
Scope and limitations
- The ledger concerns the stated included spectrum and channels. It does not automatically settle all consistency conditions of a higher-dimensional completion.
- A nonzero bulk contribution may be cancelled by suitable boundary matter; this page alone does not provide that completion.
- Anomaly cancellation is not an experimental acceptance test.
If something is unclear
The total is zero but the verdict says no subject.
Inspect the fermion list. There may be no relevant massless chiral fields to test.
A nonzero channel remains.
Record its normalization and contributors before adding boundary matter; cancellation must be checked with matching conventions.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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