Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model

In the infrared limit, a nearly anti-de Sitter spacetime in two dimensions (AdS${}_2$) perturbed by a weak double trace deformation and a two-site $(q>2)$-body Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas and a weak $2r$-body intersite coupling share the same near-conformal dynamics described by a traversable wormhole. We exploit this relation to propose a symmetry classification of traversable wormholes depending on $N$, $q$, and $r$, with $q>2r$, and confirm it by a level statistics analysis using exact diagonalization techniques. Intriguingly, a time-reversed state never results in a new state, so only six universality classes occur: A, AI, BDI, CI, C, and D.