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arxiv: 2604.07449 · v2 · submitted 2026-04-08 · ✦ hep-th

Quantum Fluctuations and Newton-Cartan Geometry for Non-Relativistic de Sitter space

Matthias Harksen , Diego Hidalgo , Watse Sybesma This is my paper

Pith reviewed 2026-05-10 17:41 UTC · model grok-4.3

classification ✦ hep-th
keywords non-relativistic de Sitter gravitySchwarzian actionquantum fluctuationsNewton-Cartan geometryone-loop partition functionOstrogradsky formalismJT gravitynon-relativistic holography
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The pith

The one-loop partition function of the non-relativistic Schwarzian action for de Sitter gravity produces a temperature-dependent prefactor scaling as T squared.

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

The paper studies a non-relativistic version of two-dimensional de Sitter gravity in both boundary and bulk formulations. On the boundary it evaluates the one-loop partition function of the associated Schwarzian-type action by deriving the path integral measure directly from the action via the Ostrogradsky formalism rather than coadjoint orbits. This computation yields a prefactor that scales with the square of temperature, and the exponent matches the number of global symmetry generators present in the theory. In the bulk it constructs a torsionless Newton-Cartan geometry that satisfies the equations of motion of a non-relativistic JT-like action and can be lifted to three-dimensional Lorentzian geometry. A reader would care because the result supplies an explicit handle on quantum effects in de Sitter space through a non-relativistic lens and demonstrates a concrete route toward non-relativistic holographic dualities.

Core claim

The central claim is that the one-loop partition function of the non-relativistic Schwarzian boundary action, computed with a path-integral measure obtained from the Ostrogradsky formalism, contains a temperature-dependent prefactor that scales as T squared, with the power agreeing with the counting of the four global symmetry generators, while the corresponding bulk description is a torsionless Newton-Cartan geometry obeying the equations of a non-relativistic JT-like action that uplifts to three-dimensional Lorentzian geometry.

What carries the argument

The Ostrogradsky formalism applied to the higher-derivative Schwarzian action, which supplies the path-integral measure used to extract the one-loop quantum fluctuations and their T squared prefactor.

Load-bearing premise

The Ostrogradsky-derived path-integral measure correctly captures the quantum fluctuations of the non-relativistic Schwarzian action without hidden gauge-fixing or measure anomalies that would alter the T squared scaling.

What would settle it

An independent computation of the same one-loop partition function by the coadjoint-orbit method that yields a temperature power different from two would falsify the central boundary result.

read the original abstract

We study a non-relativistic realisation of two-dimensional de Sitter gravity both from its boundary and bulk description with the goal of learning about de Sitter space and paving the way for extending the holographic duality into a non-relativistic direction. On the boundary side, we analyse the Schwarzian-type boundary action associated with non-relativistic de Sitter gravity and evaluate its one-loop partition function in order to compute its quantum fluctuations. Rather than relying on the coadjoint-orbit construction, we derive the path integral measure directly from the action using the Ostrogradsky formalism. We find a temperature-dependent prefactor scaling as $T^2$, of which the power agrees with the counting of the four global symmetry generators present. On the bulk side, we construct the corresponding torsionless Newton-Cartan geometry and show that it satisfies the equations of motion of a non-relativistic JT-like action and uplift the geometry to a three-dimensional Lorentzian geometry.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript studies non-relativistic two-dimensional de Sitter gravity from boundary and bulk viewpoints. On the boundary, it examines the Schwarzian-type action and computes its one-loop partition function by deriving the path-integral measure directly from the action via the Ostrogradsky formalism (rather than coadjoint orbits), obtaining a temperature-dependent prefactor scaling as T² whose power matches the four global symmetry generators. On the bulk side, it constructs the corresponding torsionless Newton-Cartan geometry, verifies that it satisfies the equations of motion of a non-relativistic JT-like action, and uplifts the geometry to three-dimensional Lorentzian space.

Significance. If the Ostrogradsky-derived measure is shown to be free of additional Jacobians or anomalies, the work supplies an independent route to the one-loop prefactor in non-relativistic Schwarzian theories and thereby strengthens the foundations for non-relativistic holographic dualities involving de Sitter space. The explicit bulk geometric construction and its consistency with the equations of motion provide a useful cross-check. The agreement between the computed power and the symmetry-generator count is a concrete, falsifiable feature that adds value if the measure derivation is fully controlled.

major comments (1)
  1. [Boundary analysis and one-loop partition function] The central claim that the Ostrogradsky reduction yields a measure whose functional determinant (or zero-mode factors) produces precisely a T² prefactor with no extra T-dependent contributions from auxiliary momenta, gauge redundancies, or regularization artifacts is load-bearing for the reported result. Explicit verification of the phase-space measure, including any Fadeev-Popov or Jacobian factors tied to the four global symmetries, is required before the numerical agreement with generator counting can be regarded as confirmatory.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the major comment on the boundary analysis below and will revise the manuscript to provide the requested explicit details on the phase-space measure.

read point-by-point responses

  1. Referee: The central claim that the Ostrogradsky reduction yields a measure whose functional determinant (or zero-mode factors) produces precisely a T² prefactor with no extra T-dependent contributions from auxiliary momenta, gauge redundancies, or regularization artifacts is load-bearing for the reported result. Explicit verification of the phase-space measure, including any Fadeev-Popov or Jacobian factors tied to the four global symmetries, is required before the numerical agreement with generator counting can be regarded as confirmatory.

    Authors: We agree that making the verification of the phase-space measure fully explicit strengthens the result. In the manuscript we derive the path-integral measure directly from the action via the Ostrogradsky formalism; this procedure reduces the phase space while incorporating the auxiliary momenta and the second-class constraints inherent to the action. The resulting T² prefactor is generated by the four zero modes associated with the global symmetries. To address the concern about possible additional contributions, we will revise the manuscript to include a detailed computation of the full phase-space measure. This will explicitly evaluate the Jacobian arising from the Ostrogradsky coordinate transformation, compute the Fadeev-Popov determinant for the four global symmetries, and demonstrate that regularization artifacts do not introduce further T-dependent factors. We expect this addition to confirm that the prefactor remains precisely T². revision: yes

Circularity Check

0 steps flagged

No significant circularity; Ostrogradsky measure derivation is independent

full rationale

The paper derives the path-integral measure for the non-relativistic Schwarzian action directly via the Ostrogradsky formalism applied to the higher-derivative boundary action, explicitly avoiding the coadjoint-orbit construction. The resulting T² prefactor is obtained from this computation and separately noted to agree with the count of four global symmetry generators, but the derivation itself does not reduce to or presuppose that counting. No load-bearing self-citations, fitted inputs renamed as predictions, or ansatz smuggling appear in the central chain. The bulk Newton-Cartan geometry construction is a separate analysis and does not feed back into the boundary fluctuation result. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions of two-dimensional gravity theories plus the specific non-relativistic limit; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The non-relativistic limit of two-dimensional de Sitter gravity admits a well-defined Schwarzian-type boundary action whose higher-derivative terms can be handled by the Ostrogradsky formalism without anomalies.
    Invoked when the boundary action is introduced and the measure is derived.
  • domain assumption A torsionless Newton-Cartan geometry in two dimensions can be uplifted to a three-dimensional Lorentzian geometry while preserving the equations of motion of the non-relativistic JT-like action.
    Stated when the bulk geometry is constructed and verified.

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