The Riemann-Lebesgue Lemma, D=11/ D=10 SuperGravity Actions, and Fourier Analysis

In my last post, I used the GKP-Witten relation {Z_{CFT}} = {e^{ - {S_{GRAVITY}}}}({\phi _i}) to solve to ‘Ricci/dilaton’ problem for the action of supergravity, since the holographic formula derived

    \[{S_A} = \frac{{\left| {{\gamma _A}} \right|}}{{4G_N^3}} = \frac{{\frac{{3R}}{{2G_N^{(3)}}}}}{3}{\rm{log}}\left( {\frac{{{l_s}}}{g}} \right)\]

with {l_s} being the string length, allowed us to compute the Matsubara frequencies

AdS/CFT Duality, GKP-Witten Relation, and U(1)-Symmetric Holography

All high mathematics serves to do is to beget higher mathematics. ~ Ashim Shanker!

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. W. S. Anglin, in Mathematics and History