arxiv: 2604.21408 · v2 · submitted 2026-04-23 · ✦ hep-th · gr-qc

Recognition: unknown

Holographic complexity of conformal fields in global de Sitter spacetime

Sanhita Parihar , Shubho R. Roy

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:49 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords holographic complexityde Sitter spacetimeconformal field theoryAdS/CFTvolume prescriptionaction prescriptionglobal coordinatesbrane embedding

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The pith

Holographic complexity for conformal fields on global de Sitter spacetime is computed using volume and action prescriptions in two AdS embeddings.

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

This paper computes the holographic complexity of conformal quantum fields on rigid global de Sitter spacetime using the volume and action prescriptions of AdS/CFT. It examines two setups: AdS spacetime foliated by global de Sitter slices with the CFT on the conformal boundary, and a global de Sitter brane embedded in AdS with the CFT on the brane. Results from these global coordinate approaches are compared to each other and to earlier calculations performed in static or Poincaré patches of de Sitter space. A reader would care because these computations test how quantum complexity behaves in an expanding cosmological background where standard holographic dictionaries are less settled.

Core claim

In the first setup, AdS_{d+1} is foliated by global dS_d slices and the complexity of the boundary CFT is obtained from the bulk volume and action functionals. In the second setup, a global dS_d UV brane is placed in AdS_{d+1} and the same functionals yield the complexity of the CFT living on the brane. Explicit time-dependent expressions are derived in both cases and contrasted with literature results obtained in alternative coordinate patches.

What carries the argument

The volume prescription (maximal volume of a bulk slice) and action prescription (on-shell action in a Wheeler-DeWitt patch) applied to AdS geometries foliated by or containing global de Sitter slices.

If this is right

The complexity grows with time in a manner that depends on whether the CFT is placed on the AdS boundary or on an embedded de Sitter brane.
Global de Sitter patches produce complexity values distinct from those found in static or Poincaré patches, indicating sensitivity to the choice of foliation.
The brane construction supplies an independent UV-regulated definition of complexity that can be compared directly to the boundary definition.
These explicit expressions serve as reference points for any future holographic model that includes dynamical gravity or matter on de Sitter slices.

Where Pith is reading between the lines

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

If the global-coordinate results survive further checks, they suggest that holographic complexity can be defined consistently even when the boundary geometry has positive curvature, potentially extending the dictionary to more realistic cosmologies.
Differences between the boundary and brane setups may correspond to different choices of time slicing or reference states, offering a way to test how complexity depends on the observer's frame in de Sitter space.
The computations could be extended by adding bulk matter or considering the back-reaction of the brane tension to see whether the complexity formulas remain stable.

Load-bearing premise

The standard volume and action complexity prescriptions remain valid when applied to rigid global dS backgrounds and to the chosen AdS foliation or brane embeddings without additional dS-specific corrections.

What would settle it

A field-theory calculation of state complexity for a CFT on global de Sitter that produces a different time dependence or magnitude than the holographic expressions obtained here would falsify the results.

read the original abstract

We compute the holographic complexity of conformal quantum fields in rigid global de Sitter spacetime (dS$_{d}$) using the volume and action prescriptions. First we consider AdS$_{d+1}$ spacetime in global dS$_{d}$ foliations, and compute the complexity of the CFT supported on the global dS$_{d}$ conformal boundary. Next, we consider CFT supported on a global dS$_d$ (UV) brane embedded in AdS$_{d+1}$ spacetime, and compute the holographic complexity in this brane set up. We compare and contrast the results in the two cases, as well as with related results in the literature obtained in alternative holographic set ups involving patches of de Sitter spacetime covered by static coordinates or conformal (Poincar\'e) coordinates.

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

Computes explicit CV and CA results for global dS foliations and branes but applies unmodified AdS prescriptions without addressing possible dS corrections.

read the letter

The one thing to know is that this paper calculates holographic complexity for CFTs in global de Sitter using the volume and action prescriptions in AdS setups with global dS foliations and branes, then compares to static and Poincare results. It is new in the choice of global coordinates and the brane case. The paper does well by carrying out these explicit computations and laying out the differences across setups, giving concrete numbers where only other patches were available before. The soft spot is the assumption that the standard prescriptions work without changes. These were developed for AdS, and global dS has positive curvature and a different causal structure that could affect the extremal surfaces or boundary terms. The abstract gives no derivations or checks, so the results depend on whether the full paper justifies this transplant or tests it. If it does not, the comparisons may not hold up. This work is for people already in the holographic complexity community who care about de Sitter applications. It will not shift the field but provides useful reference calculations. It deserves peer review because the computations are new and fill a specific gap, though a referee should examine the validity of the prescriptions in this context. I recommend sending it to review.

Referee Report

1 major / 2 minor

Summary. The paper computes the holographic complexity of conformal quantum fields in rigid global de Sitter spacetime (dS_d) using the volume (CV) and action (CA) prescriptions. It first considers AdS_{d+1} spacetime in global dS_d foliations to compute the complexity of the CFT supported on the global dS_d conformal boundary. Next, it examines the CFT supported on a global dS_d (UV) brane embedded in AdS_{d+1} spacetime and computes the holographic complexity in this brane setup. The results are compared and contrasted with each other as well as with related results in the literature obtained in alternative holographic setups involving patches of de Sitter spacetime covered by static coordinates or conformal (Poincaré) coordinates.

Significance. If the central claims hold, this work extends holographic complexity calculations to global de Sitter coordinates, filling a gap relative to the more commonly studied static and Poincaré patches and providing a more cosmologically relevant setting. The dual setups (boundary CFT and UV brane) enable useful comparisons. Credit is given for performing explicit computations in these foliations and for contrasting the outcomes across coordinate choices.

major comments (1)

[Holographic setups and prescriptions] The load-bearing assumption that the standard CV and CA prescriptions (originally derived for asymptotically AdS spacetimes) can be applied without dS-specific corrections to the counterterms, extremal surfaces, or action boundary terms in global dS_d foliations of AdS_{d+1} requires explicit justification. The positive cosmological constant, cosmological horizons, and altered causal structure could introduce modifications that would affect the reported complexity values and their comparison to static/Poincaré results.

minor comments (2)

[Abstract] The abstract states that computations were performed but would benefit from a brief mention of the key analytic or numerical methods, error estimates, or consistency checks against known limits (e.g., flat-space or small-dS-radius regimes) to aid quick assessment.
Ensure that all notation for the foliation parameters, brane embeddings, and complexity functionals is defined consistently on first use, and consider adding a table summarizing the complexity expressions across the two setups and coordinate patches for clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback. We address the major comment below.

read point-by-point responses

Referee: The load-bearing assumption that the standard CV and CA prescriptions (originally derived for asymptotically AdS spacetimes) can be applied without dS-specific corrections to the counterterms, extremal surfaces, or action boundary terms in global dS_d foliations of AdS_{d+1} requires explicit justification. The positive cosmological constant, cosmological horizons, and altered causal structure could introduce modifications that would affect the reported complexity values and their comparison to static/Poincaré results.

Authors: We appreciate the referee raising this point. Our setups employ AdS_{d+1} as the bulk geometry (with negative cosmological constant), using global dS_d foliations merely as a coordinate choice on the boundary or on the UV brane. The CV and CA prescriptions, including their counterterms and boundary terms, are defined and evaluated entirely in the asymptotically AdS bulk, whose causal structure is unaffected by the foliation. The positive cosmological constant, cosmological horizons, and associated features belong to the boundary CFT or the brane itself, not the bulk spacetime in which the extremal surfaces and Wheeler-DeWitt patches are constructed. Therefore, no dS-specific corrections are required, and the results remain directly comparable to those obtained in static or Poincaré patches of dS. We will add an explicit paragraph in the revised manuscript (likely in Section 2 or the introduction) justifying this application of the standard prescriptions and clarifying why the bulk AdS properties ensure no modifications are needed. revision: yes

Circularity Check

0 steps flagged

No circularity: direct computations using standard CV/CA prescriptions on dS foliations

full rationale

The paper applies the established volume (CV) and action (CA) holographic complexity prescriptions to AdS_{d+1} geometries with global dS_d foliations and UV brane embeddings. These are standard external prescriptions from prior AdS/CFT literature, not redefined or fitted within the paper. The derivations consist of explicit calculations of complexity for the CFT on the dS boundary and brane, followed by comparisons to other coordinate patches in the literature. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or described chain. The central results are independent computations under the stated assumptions, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are identifiable from the given text. The work implicitly relies on standard holographic duality and the applicability of complexity prescriptions to dS.

pith-pipeline@v0.9.0 · 5434 in / 1117 out tokens · 32986 ms · 2026-05-09T21:49:22.349054+00:00 · methodology

discussion (0)

Reference graph

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