Brane kinetic terms
What happens to the tower when brane-localised kinetic terms make the masses stop being n/R.
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 see how kinetic terms localized at a boundary change a Kaluza–Klein mass equation and its roots. The zero-boundary-coefficient limit provides a useful check against a simpler tower. The warped SU(6) running card is a separate experiment and has its own inputs and guide.
First steps
- Use the Warped SU(6) shortcut to compare C1/C2 differential running, required UV brane terms and the separate localization probe.
- Set the brane coefficient.
- Read the roots of the transcendental mass equation.
- Take the coefficient to zero and watch the ordinary twisted tower come back.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Brane coefficient c | Controls the boundary kinetic contribution in the displayed mass equation. | Compare a nonzero value with c = 0. |
| α₁ and α₂ | The displayed phase parameters of this spectral example; retain its normalization when comparing another model. | Vary one phase while holding c fixed. |
| m and q | The additional mass/charge parameters defined by the equation on the page. | Read their role in the equation before changing both together. |
| Demonstration / Warped SU(6) shortcut | Run the guided spectral example or open the separate differential-running experiment. | Use the demonstration first to connect the equation with its root plot. |
Reading the results
| Result | Meaning |
|---|---|
| Mass-equation roots | The allowed levels of the stated boundary problem; they need not be integer-spaced. |
| Tower view | Displays the same roots as a spectrum rather than as intersections of the mass equation. |
| Zero-coefficient comparison | Checks the solver against the ordinary twisted-tower limit under the same parameters. |
The special functions are checked against mpmath at forty digits, and the c → 0 limit is computed in closed form by code that shares nothing with the solver. That limit found three real defects.
Worked example
Recover a known limit
- Run the supplied demonstration.
- Record a few roots at nonzero c.
- Bring c to zero while keeping the phases fixed.
- Compare the resulting tower with the displayed closed-form limit.
What to expect: The numerical spectrum connects continuously to the stated reference limit where that limit applies.
Scope and limitations
- This is the supported spectral boundary problem, not a complete scan of all boundary operators.
- A solver check does not establish every physical consistency property of an arbitrary kinetic-term choice.
- The warped SU(6) running experiment is not a result computed from these spectral controls.
If something is unclear
The tower is no longer equally spaced.
Read the modified mass equation; the boundary kinetic term changes the root condition.
Two cases have different limits.
Compare phases, m, q and normalization as well as the coefficient c.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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