Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity

Eleonora Alfinito; Matteo Beccaria

arxiv: 2606.20220 · v3 · pith:7FUTS6BWnew · submitted 2026-06-18 · ✦ hep-th

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity

Eleonora Alfinito , Matteo Beccaria This is my paper

Pith reviewed 2026-06-26 16:02 UTC · model grok-4.3

classification ✦ hep-th

keywords wormhole lengthsine-dilaton gravityDSSYKKrylov complexitysemiclassical expansionLiouville equationshigher-loop correctionscumulants

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The pith

Quantum wormhole length in sine-dilaton gravity equals Krylov spread complexity of the double-scaled SYK model at five-loop order.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the quantum wormhole length equals the Krylov spread complexity in the double-scaled SYK model. It computes the five-loop semiclassical expansion of this complexity at infinite temperature by applying singular perturbation to the operator Liouville-type equations of motion. The same technique yields the Krylov variance and third cumulant, which correspond to connected correlation functions of the length operator. Small- and large-time regimes are analyzed, including an all-order resummation of the perturbative series for the large-time linear growth slope together with leading non-perturbative corrections.

Core claim

The length of the quantum wormhole in sine-dilaton gravity is identical to the Krylov spread complexity in the double-scaled SYK model; this identification permits a systematic five-loop semiclassical computation of the complexity via singular perturbation of the associated operator Liouville equations, together with the variance, third cumulant, and an all-order resummation of the large-time slope.

What carries the argument

Singular perturbation applied to the operator Liouville-type equations of motion, which generates the semiclassical loop expansion of the Krylov complexity.

If this is right

The five-loop result supplies concrete higher-order corrections to the wormhole length at infinite temperature.
The method also determines the connected two- and three-point functions of the length operator via the variance and third cumulant.
An all-order resummation exists for the coefficient of linear growth of the wormhole length at late times.
Leading non-perturbative corrections to the same large-time slope can be extracted from the same framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the identification persists, numerical evaluation of Krylov complexity in finite-N SYK chains could supply quantitative predictions for wormhole lengths that are otherwise difficult to access in gravity.
The singular-perturbation technique may extend to other observables that admit a Liouville-type operator description, such as higher moments of the length distribution.
The all-order resummation of the slope suggests that the late-time growth rate admits a closed-form expression independent of loop order.

Load-bearing premise

The equality between wormhole length and Krylov spread complexity remains valid at every order in the semiclassical expansion.

What would settle it

An explicit mismatch between the five-loop perturbative terms obtained from the DSSYK equations and the corresponding wormhole-length observables computed directly in sine-dilaton gravity would disprove the identification.

Figures

Figures reproduced from arXiv: 2606.20220 by Eleonora Alfinito, Matteo Beccaria.

**Figure 2.** Figure 2: Left panel: small time behaviour of the Krylov complexity at J “ 1 and q “ 1 ´ 1{4. The black dashed line is the result of integration of (2.21) with a truncated Krylov basis with 103 states. The red line is the quadratic function 1 1´q pJ tq 2 . The green line is our expansion in (8.1). Right panel: large time behaviour of the Krylov complexity at J “ 1 and q “ 1 ´ 1{4. The black dashed line is the result… view at source ↗

**Figure 3.** Figure 3: Comparison between the numerically estimated slope [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗

read the original abstract

The quantum wormhole length in sine-dilaton gravity has been shown to equal the Krylov spread complexity in the double-scaled SYK model. In the infinite temperature limit, we compute the five-loop semiclassical expansion of DSSYK complexity by singular perturbation of the operator Liouville-type equations of motion, extending the existing one-loop results. The same method is applied to evaluate the Krylov variance and third-order cumulant, related to the connected two- and three-point functions of the length operator at coincident points. The small- and large-time behaviour of these observables is also studied. In particular, for the large-time slope of the wormhole linear growth, we determine the all-order resummation of the perturbative series, and the leading non-perturbative corrections.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper extends the one-loop DSSYK complexity calculation to five loops via singular perturbation and adds a large-time resummation, all under the wormhole-length identification from earlier work.

read the letter

The main new material is the five-loop semiclassical expansion of the Krylov spread complexity in the infinite-temperature DSSYK model, obtained by singular perturbation of the operator Liouville equations. The authors also extract the variance and third cumulant (tied to connected correlators of the length operator) and give the all-order resummation of the large-time linear growth plus leading non-perturbative corrections. These steps are presented as a direct continuation of the one-loop results already in the literature.

The calculation looks technically consistent on its own terms. The method is applied uniformly to the complexity, its moments, and the time regimes, and the resummation is a concrete output that goes beyond finite-order perturbation. If the underlying operator equations and the singular-perturbation procedure are handled without omitted terms, the five-loop coefficients and the resummed slope are usable results inside this narrow corner of holographic models.

The central assumption remains the identification of wormhole length with Krylov complexity, taken from prior papers and assumed to hold order by order. The soundness therefore rests on whether that mapping survives the higher-loop corrections and whether the perturbation captures every contribution without model-specific adjustments. No internal contradiction appears in the stated approach, but the absence of explicit error estimates or cross-checks against other methods leaves the numerical reliability of the five-loop terms unverified from the abstract alone.

This is a specialized computation for readers already working on DSSYK, sine-dilaton gravity, or Krylov complexity in holography. It supplies concrete higher-order expressions rather than a new conceptual framework, so its value is mainly to those who need the explicit coefficients or the resummed large-time behavior. The work is coherent enough to merit referee time; a serious editor should send it out rather than desk-reject it.

Referee Report

0 major / 1 minor

Summary. The paper claims that the quantum wormhole length in sine-dilaton gravity equals the Krylov spread complexity in the double-scaled SYK model. In the infinite temperature limit, it computes the five-loop semiclassical expansion of DSSYK complexity via singular perturbation of the operator Liouville-type equations of motion, extending prior one-loop results. The same method is used to evaluate the Krylov variance and third-order cumulant (related to connected two- and three-point functions of the length operator at coincident points), along with small- and large-time behaviors; an all-order resummation of the perturbative series is given for the large-time slope of the wormhole linear growth, together with leading non-perturbative corrections.

Significance. If the wormhole-length/Krylov-complexity identification persists order-by-order, the manuscript supplies a concrete higher-order verification and extension in a solvable holographic model. Credit is due for the five-loop computation, the application of singular perturbation to operator equations, the extraction of higher cumulants, and especially the all-order resummation of the linear-growth slope together with non-perturbative corrections; these constitute technical advances that furnish explicit data for testing the correspondence beyond one loop.

minor comments (1)

The relation between the length operator cumulants and the connected correlation functions is stated in the abstract but would benefit from an explicit equation or short derivation in the main text (e.g., near the definition of the cumulants) to make the mapping fully transparent.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, their recognition of the technical contributions including the five-loop computation and all-order resummation, and their recommendation to accept. There are no major comments requiring a point-by-point response.

Circularity Check

0 steps flagged

No circularity; new perturbative computation extends external identification

full rationale

The paper cites the wormhole length = Krylov complexity equality as previously shown in the literature and performs an independent five-loop computation of DSSYK complexity via singular perturbation of the operator Liouville equations, extending one-loop results. No step reduces by construction to a fitted input, self-definition, or load-bearing self-citation chain; the higher-order terms and resummations are derived from the perturbation method itself. The assumption that the identification holds order-by-order is an external modeling choice, not an internal circular reduction. The derivation chain for the new observables is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no explicit free parameters, axioms, or invented entities can be extracted. The mapping between gravity and SYK quantities is presupposed from earlier work.

pith-pipeline@v0.9.1-grok · 5662 in / 1250 out tokens · 21375 ms · 2026-06-26T16:02:53.975963+00:00 · methodology

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity

Core claim

What carries the argument

If this is right

Where Pith is reading between the lines

Load-bearing premise

What would settle it

discussion (0)