2026/07/23 by José L. F. Barbón, Eduardo Velasco-Aja
#hep-th
We analyze the contribution of AdS black hole saddles to the spectral form factor of d-dimensional CFTs with a gravity dual. At high temperatures, the analytically continued gravitational action of the large AdS black hole is expected to give a leading large-N approximation to the 'slope' of the spectral form factor. When the CFT is put on a (d-1)-dimensional spatial sphere of radius ℓ, we show that such an evaluation implies unphysical behavior of Z(β+it) at large t≫ ℓ for d≡5 (\rm mod 4). A Picard--Lefschetz analysis of a minisuperspace approximation to Z(β+it) does reveal the required Stokes phenomena that restore consistency. It is found that for d>3, the large AdS black hole saddle loses dominance and subsequently disconnects from the relevant integration cycle at t=O(β). For d=3, dominance is lost at a time of order β, while the Stokes disconnection takes place at t=O(ℓ). After the large black hole saddle disconnects from the path-integral contour, the slope of the spectral form factor becomes dominated by the low-energy end of the spectrum.