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arXiv:2203.14988 · Physical review. D/Physical review. D.

Wormholes and half wormholes under irrelevant deformation

Diptarka Das, Sridip Pal, Anurag Sarkar

Published Sep 15, 2022• 7 citations
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Abstract

Recently it has been shown by Almheiri and Lin [1] that the reconstruction of a 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 Sachdev-Ye-Kitaev by deforming the same with ``irrelevant'' coupling. We find that half-wormholes, as well as the wormholes, persist in the 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) Sachdev-Ye-Kitaev we find nontrivial 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.

DOI
10.1103/physrevd.106.066014

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Recently it has been shown by Almheiri and Lin [1] that the reconstruction of a 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 Sachdev-Ye-Kitaev by deforming the same with ``irrelevant'' coupling. We find that half-wormholes, as well as the wormholes, persist in the 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) Sachdev-Ye-Kitaev we find nontrivial 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.
The Sachdev--Ye--Kitaev (SYK) model has a wormholelike solution after averaging over the fermionic couplings in the nearly AdS2{\mathrm{AdS}}_{2}AdS2​ space. Even when the couplings are fixed the contribution of these wormholes continues to exist and new saddle points appear which are interpreted as ``half-wormholes.'' In this paper, we will study the fate of these wormholes in a model without quenched disorder, namely, a tensor model with $O(N{)}^{q\ensuremath{-}1}$ gauge symmetry whose correlation function and thermodynamics in the large NNN limit are the same as that of the SYK model. We will restate the factorization problem linked with the wormhole threaded Wilson operator, in terms of global charges or nontrivial cobordism classes associated with disconnected wormholes. Therefore for the partition function to factorize especially at short distances, there must exist certain topological defects which break the global symmetry associated with wormholes and make the theory devoid of global symmetries. We will interpret these wormholes with added topological defects as our ``half-wormholes.'' We will also comment on the late time behavior of the spectral form factor, particularly its leading and subleading order contributions coming from higher genus wormholes in the gravitational sector. Finally we will show how the other nontrivial saddles from half-wormhole dominate and give rise to unusual thermodynamics in the bulk sector due to nonperturbative effects.
In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a ``wormhole'' saddle plus a ``pair of linked half-wormholes'' saddle. It explains factorization of decoupled systems. Here, we derive an explicit formula for the half-wormhole contribution. It is expressed through a hyperpfaffian of the tensor of SYK couplings. We then develop a perturbative expansion around the half-wormhole saddle. This expansion truncates at a finite order and gives the exact answer. The last term in the perturbative expansion turns out to coincide with the wormhole contribution. In this sense the wormhole saddle in this model does not need to be added separately, but instead can be viewed as a large fluctuation around the linked half-wormholes.
A bstract After averaging over fermion couplings, SYK has a collective field description that sometimes has “wormhole” solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space — “half-wormholes.” The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.
Abstract In this paper, we introduce a “partially disorder-averaged” SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.
In the Sachdev-Ye-Kitaev (SYK) model, traversable wormhole teleportation fidelity probes the many-body scrambling of holographic black holes. We apply a gravitational-wave-inspired periodic Floquet deformation derived from the lowest-dimensional bilinear SYK4\text{SYK}_4SYK4​ sector to the boundary, thereby characterizing the channel response via exact numerical time evolution at βJ=2βJ = 2βJ=2. Re-optimizing under the drive isolates genuine physical effects from calibration mismatch, yielding four main results: (i) distinct perturbative and non-perturbative amplitude regimes separated near ε∼J\varepsilon \sim Jε∼J; (ii) a natural low-pass filter response, with maximum fidelity suppression at ω≲β−1ω\lesssim β^{-1}ω≲β−1 and monotonic recovery above the thermal scale; (iii) a scrambling delay, evidenced by a delayed fidelity peak under an inspiral chirp (Δtscr(fid)=+0.11 J−1Δt_{\mathrm{scr}}^{(\mathrm{fid})} = +0.11\, J^{-1}Δtscr(fid)​=+0.11J−1) and independently confirmed by OTOC measurements to grow monotonically with drive amplitude; and (iv) robust, non-zero fidelity suppression across N∈{10,12,14,16}N \in \{10, 12, 14, 16\}N∈{10,12,14,16} Majorana modes. These findings establish that holographic wormholes degrade gracefully under metric-like boundary deformations, providing direct diagnostic signatures for near-term quantum hardware.
Abstract The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. We sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. The entanglement wedge of the reference can then be interpreted as the bulk region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity + a matter BCFT, the QES formula implies that the reference contains the black hole interior at late times. We also analyze the Renyi-2 entropy tr ρ2 of the reference, which can be viewed as a diagnostic of chaos via the Loschmidt echo. We find explicitly the replica wormhole that diagnoses the island and restores unitarity. Numerical and analytical evidence of these statements in the SYK model is presented. Similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings.