Coarse graining from within: Wilson-Fisher universality on $S^3$ (opens in new tab)

Wilsonian renormalization is usually formulated in momentum space, but on curved backgrounds momentum shells have no invariant meaning. We replace them by an intrinsic spectral cutoff, ordering modes by the covariant Laplacian and setting the cutoff resolution by the system size in renormalization group (RG) units. For a scalar field on $S^3$, this yields a covariant, momentum-free RG flow whose trace is an exact sum over spherical harmonics. ...