Clarify the effect of rotating fuzzy extra dimensions

Determine how a nonzero R charge of the fuzzy extra-dimensional background modifies the Kaluza–Klein spectrum and whether it selects physically acceptable compact fuzzy backgrounds.

Background

The stabilization mechanism adopted in the paper uses a large R charge for the fuzzy extra dimensions. Such a charge is expected to influence the Kaluza–Klein sector and may be relevant for obtaining realistic low-energy physics.

The one-loop Einstein–Hilbert calculation cited in the paper assumes a static internal space, so the effects of the time-dependent R-charge configuration remain unresolved.

References

Since it is not clear which spin is picked out by our calculation, we remain agnostic on whether it is spin zero or two.

— Monopoles, duality, and large charge in Chern-Simons QED$_3$  (2609.37795 - Chester et al., 29 Sep 2026) in Section 1, Introduction, discussion following Eq. (m1)

A nontrivial $R$ charge of $K$ will have some nontrivial effects on the KK spectrum, which remains to be clarified. This may also lead to a selection of acceptable $K$ backgrounds.

— Quantum spacetime and gravity from the IKKT matrix model: an invitation  (2609.08955 - Steinacker, 8 Sep 2026) in Section 6, “Compact extra dimensions”