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The SYK model has a wormhole-like solution after averaging over the fermioniccouplings in the nearly $AdS_2$ space. Even when the couplings are fixed thecontribution of these wormholes continues to exist and new saddle points appearwhich are interpreted as "half-wormholes". In this paper, we will study thefate of these wormholes in a model without quenched disorder namely a tensormodel with $O(N)^{q-1}$ gauge symmetry whose correlation function andthermodynamics in the large $N$ limit are the same as that of the SYK model. Wewill restate the factorization problem linked with the wormhole threaded Wilsonoperator, in terms of global charges or non-trivial cobordism classesassociated with disconnected wormholes. Therefore for the partition function tofactorize especially at short distances, there must exist certain topologicaldefects which break the global symmetry associated with wormholes and make thetheory devoid of global symmetries. We will interpret these wormholes withadded topological defects as our "half-wormholes". We will also comment on thelate time behavior of the spectral form factor, particularly its leading andsub-leading order contributions coming from higher genus wormholes in thegravitational sector. Finally we will show how, the other non-trivial saddlesfrom "half-wormhole" dominate and give rise to unusual thermodynamics in thebulk sector due to non-perturbative effects.

Wormhole calculus without averaging from $O(N)^{q-1}$ tensor model