Gravity–gauge · 3D
Which physical information a complete tower of masses leaves undetermined in a controlled gravity-gauge example.
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 controlled example to distinguish knowing an entire sequence of masses from knowing how a source couples to those states. The paired mass towers can stay fixed while source residues and the Wilson kinetic scale change. The second, unprotected gauge tower provides a comparison with different boundary conditions.
First steps
- Start with p=1.1 and press eta=-0.9, eta=0, then eta=4. The paired masses stay equal while the Wilson scale and the response change.
- Drag either 3D plot to turn it. On the response surface, switch drag to select point to change eta and the source position together. Shift-drag always turns; the wheel changes relief; arrow keys turn a focused plot.
- Read the table below the plots. Choose gauge kinetic Z as the height to inspect the action. Use the header card or LaTeX buttons to export this exact input, or link to restore it.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Geometry p | Selects the displayed background; p = 1.1 is the scalar-supported example and p = 1 the AdS reference. | Begin at p = 1.1. |
| η and log₁₀(1 + η) | Two ways to select the positive gauge-kinetic family parameter in its supported range. | Compare the η = −0.9, 0 and 4 presets. |
| Source t | A position along the extra dimension, not a location in a laboratory detector. | Move the source while comparing spectral weight with mass. |
| Height, drag mode and 3D controls | Choose spectral-weight ratio or Z(t); drag to rotate or select a point. Shift-drag rotates, the wheel changes relief, and focused plots accept arrow keys. | Select a point on the response surface, then read its exact table values. |
Reading the results
| Result | Meaning |
|---|---|
| Paired tensor NN and vector DD masses | The protected comparison governed by the shared canonical operator and stated boundary conditions. |
| Vector NN control | Uses different boundary conditions and need not keep the same masses. |
| Response and Wilson kinetic scale | Additional information that is not fixed by the paired masses alone; the Wilson kinetic scale is not a Higgs mass. |
The positive paired tensor NN and vector DD masses are protected by their common canonical operator. The gauge NN control has different boundaries and moves. The source position is in the extra dimension, not a laboratory location; the Wilson kinetic scale is not a Higgs mass. For p=1.1 a canonical bulk scalar realizes the family, with stability and cutoff still open.
Worked example
Hold the paired masses while changing the response
- Set p = 1.1.
- Compare η = −0.9, 0 and 4 at a fixed source position.
- Read the paired masses and the response table at each setting.
- Move the source and save a card or permalink for the selected point.
What to expect: The protected paired towers remain equal within the implemented construction while other response information changes.
Scope and limitations
- The boundary-condition pairing is essential; it does not protect every tower.
- The construction does not calculate a Higgs mass, radion stability or collider rate.
- Stability and cutoff questions remain open for the displayed family.
If something is unclear
Dragging changes the view instead of the selected parameter.
Switch drag mode to select point; use Shift-drag when you want to rotate.
The gauge control masses move while the paired masses do not.
Check the boundary labels. The NN control is deliberately outside the protected NN/DD pairing.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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