(Half) Wormholes under Irrelevant Deformation

Abstract

Recently it has been shown by Almheiri and Lin [1] that the reconstruction of black-hole interior is sensitive to knowing the exact coupling of the boundary theory even if the coupling is irrelevant. This motivates us to enlarge the set of the one-time and two-time toy models inspired from the SYK by deforming the same with irrelevant coupling. We find that both half-wormholes as well as the wormholes persist in presence of the deformation, leading to a similar mechanism for curing the factorization problem. While for the one time case, the deformed partition function and its moments change by an overall factor, which can completely be absorbed into a renormalization of coupling, for the two time (or coupled one time) SYK we find non-trivial dynamics of the saddles as the couplings are varied. Curiously, the irrelevant deformations that we consider can also be thought of as an ensemble average over an overall scaling of the original undeformed Hamiltonian with an appropriate probability distribution, this allows for the possibility that half-wormholes may also be present in suitably defined ensemble of theories.

Half-Wormholes and Ensemble Averages

“…To proceed the computation we define the sign of a q-sequence, sgn(J A i ) = (−1) a i 1 +•••+a iq , q = 0mod(4) (G. 95) where when q = 2mod(4) the sign will be opposite. Note that here we take the a i from the indices of J A i , but what in the superscript should be the initial sites of the indices.…”

“…Interestingly, irrelevant deformation of 0-SYK model is studied in[95] where they show after deformation half-wormhole saddle survives. It is very possible that our new half-wormholes will also survive under the same irrelevant deformation.…”

Note on $T\bar{T}$ deformed matrix models and JT supergravity duals

“…Let us focus on the correlation functions of matrix model, i.e., the RHS of ( 14) and (20). In large N expansion as indicated by perturbation theory of matrix integral [31]…”

“…Here g is the genus of the double-line diagram in the matrix perturbation theory. Strictly speaking, equalities ( 14) and (20) hold only in the so-called double -scaled limit. In this limit, the 1/N is replaced by e −S 0 [31] in (25).…”

“…For higherdimensional cases, it has been explored in [14]. For lower dimension, i.e., the one-dimensional case or ordinary quantum mechanic system, which is the main interest of present work, the T T deformation was first introduced in [15,16], see also recent developments [17][18][19][20][21][22][23][24].…”