It is shown, non--rigorously, that the effective action on a Z_q factored odd spheres (lune) has a vanishing derivative at q=1. This leaves the effective action on the ordinary odd d-sphere as (minus) the value of the entanglement entropy associated with a (d-2)-sphere. Some numbers are given.
Effective action and tension renormalization for cosmic and fundamental strings
Effective actions with fixed points, (error in derivation of coefficient corrected)
Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher-derivative quantum gravity
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