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arxiv: 2604.20498 · v2 · submitted 2026-04-22 · ✦ hep-th

Recognition: unknown

Anisotropic drag force in finite-density QGP from charged rotating 5D black holes

Sergei G. Ovchinnikov
Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:07 UTC · model grok-4.3

classification ✦ hep-th
keywords holographic drag forcerotating black holesheavy quarkanisotropic plasmafinite densityKerr-AdSgauged supergravity
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The pith

In the neutral limit, the drag force on a heavy quark is purely tangential yet anisotropic unless the two rotation parameters are equal.

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

The paper computes the drag force on a heavy quark moving through a holographic plasma that carries both rotational anisotropy and finite charge density, using the dual five-dimensional charged rotating black hole. In the neutral Kerr-AdS limit an exact result is obtained with a principal Killing string, showing that the force stays tangential for any rotation parameters but becomes isotropic and viscous only when the two spins are equal. For the charged case a slow-rotation expansion is performed and the Lorentzian worldsheet regularity condition is imposed to remove integration ambiguities, producing a finite transverse drag force that connects smoothly to the neutral result. In the equal-spin sector the same regularity condition selects a unique co-rotating equilibrium quark and fixes its renormalised free-energy shift.

Core claim

In the neutral Kerr-AdS limit of the CCLP black hole the principal Killing string yields a purely tangential drag force that is generically anisotropic for arbitrary rotation parameters and reduces to the viscous form only in the equal-spin sector. In the charged CCLP background, perturbative analysis in the slow-rotation regime together with regularity of the Lorentzian worldsheet fixes the otherwise ambiguous angular integration constants, giving a finite renormalised transverse drag force with a smooth limit to the neutral case. In the equal-spin sector worldsheet regularity selects a unique co-rotating equilibrium quark and determines its renormalised free-energy shift.

What carries the argument

The principal Killing string embedding of the heavy-quark trajectory, with Lorentzian worldsheet regularity used to fix angular integration constants.

If this is right

  • The force remains tangential for any choice of the two rotation parameters.
  • Anisotropy in the drag force persists unless the two rotation parameters are exactly equal.
  • Worldsheet regularity supplies a concrete prescription that removes ambiguities in the charged rotating geometry.
  • A unique co-rotating equilibrium configuration exists when the spins are equal and its free-energy shift is finite after renormalisation.

Where Pith is reading between the lines

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

  • Directional dependence of the drag force could produce observable anisotropy in heavy-quark suppression patterns inside rotating quark-gluon plasma.
  • The same regularity method may be applied to compute other transport quantities such as diffusion constants in rotating charged plasmas.
  • If a different embedding or cutoff procedure is ultimately required, the transverse force might remain divergent or acquire a radial component not captured here.

Load-bearing premise

The principal Killing string supplies the correct embedding for the heavy quark trajectory and worldsheet regularity is the appropriate condition for fixing the integration constants in the charged background.

What would settle it

An independent calculation of the drag force that employs a different string embedding or omits the worldsheet regularity condition and obtains a non-tangential force component or a divergent transverse force would contradict the central results.

read the original abstract

We study the drag force acting on a heavy quark in a holographic plasma with rotational anisotropy and finite density. The bulk dual is the CCLP black hole of five-dimensional minimal gauged supergravity, characterised by two independent rotation parameters and electric charge. In the neutral Kerr--AdS limit, we use the principal Killing string to obtain an exact drag force for arbitrary rotation parameters. The resulting force is purely tangential but generically anisotropic, reducing to the viscous form only in the equal-spin sector. We then analyse stationary strings in the charged CCLP background perturbatively in the slow-rotation regime. A regularity analysis of the Lorentzian worldsheet fixes the angular integration constants that would otherwise remain ambiguous, yielding a finite renormalised transverse drag force with a smooth Kerr--AdS limit. We also show that, in the equal-spin sector, worldsheet regularity selects a unique co-rotating equilibrium quark and compute its renormalised free-energy shift.

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

2 major / 2 minor

Summary. The paper computes the drag force on a heavy quark in a holographic model of a rotating, finite-density plasma dual to the CCLP black hole in five-dimensional minimal gauged supergravity. In the neutral Kerr-AdS limit, an exact expression for the drag force is obtained via the principal Killing string embedding for arbitrary rotation parameters; the force is purely tangential and generically anisotropic, reducing to the viscous form only in the equal-spin sector. For the charged CCLP background, a slow-rotation perturbative analysis of stationary strings is performed, with Lorentzian worldsheet regularity used to fix otherwise ambiguous angular integration constants, yielding a finite renormalized transverse drag force that has a smooth Kerr-AdS limit. In the equal-spin sector, worldsheet regularity additionally selects a unique co-rotating equilibrium quark whose renormalized free-energy shift is computed.

Significance. If the principal Killing string embedding is the appropriate choice for the heavy-quark trajectory, the work supplies an exact result in the neutral limit together with a controlled perturbative extension to finite density and slow rotation. The exact neutral-limit computation and the systematic use of worldsheet regularity to resolve integration constants are concrete strengths that could furnish falsifiable predictions for anisotropic drag in rotating QGP.

major comments (2)
  1. [§3 (Neutral Kerr-AdS limit)] §3 (Neutral Kerr-AdS limit): The claim that the principal Killing string yields a purely tangential, generically anisotropic drag force rests on the assumption that this embedding corresponds to a heavy quark at rest in the rotating plasma frame. No derivation is given showing why this ansatz (rather than, e.g., a co-rotating straight string or a numerically solved worldsheet with prescribed asymptotic velocity) is the physically relevant trajectory; alternative embeddings could introduce a radial force component and thereby alter the reported anisotropy and the reduction to the viscous form in the equal-spin sector.
  2. [§4 (Perturbative charged CCLP analysis)] §4 (Perturbative charged CCLP analysis): The regularity condition on the Lorentzian worldsheet is invoked to fix the angular integration constants and obtain a finite renormalized transverse drag force. However, the manuscript does not provide an explicit check that the renormalized quantities remain cutoff-independent at the order considered or that the perturbative result matches the exact neutral-limit expression beyond leading order; without such verification the smoothness of the Kerr-AdS limit remains unconfirmed.
minor comments (2)
  1. [Notation] The notation for the two independent rotation parameters and the precise definition of the principal Killing vector should be collected in a single equation for clarity.
  2. [Results summary] A brief comparison table of the drag-force components in the neutral limit versus the perturbative charged case would help the reader assess the finite-density corrections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped us identify areas for clarification. We address each major comment point by point below. We plan to revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§3 (Neutral Kerr-AdS limit)] The claim that the principal Killing string yields a purely tangential, generically anisotropic drag force rests on the assumption that this embedding corresponds to a heavy quark at rest in the rotating plasma frame. No derivation is given showing why this ansatz (rather than, e.g., a co-rotating straight string or a numerically solved worldsheet with prescribed asymptotic velocity) is the physically relevant trajectory; alternative embeddings could introduce a radial force component and thereby alter the reported anisotropy and the reduction to the viscous form in the equal-spin sector.

    Authors: We appreciate the referee's observation that the physical motivation for the principal Killing string embedding was not derived explicitly in §3. This ansatz is selected because it corresponds to a stationary worldsheet aligned with the principal Killing vector of the Kerr-AdS geometry, which ensures that the heavy quark remains at rest with respect to the local co-rotating frame of the plasma (i.e., its asymptotic velocity matches the frame-dragging induced by the black hole rotation). In the non-rotating limit, the embedding reduces to the standard radial straight string used in the literature for drag force calculations. By construction, the symmetries of this embedding preclude a radial force component, yielding a purely tangential drag that is generically anisotropic except in the equal-spin sector where it reduces to the viscous form. While we maintain that this is the appropriate choice for the problem at hand (consistent with prior holographic studies of rotating plasmas), we acknowledge the lack of an explicit justification in the text. We will add a short paragraph in §3 deriving the physical relevance of the ansatz, including a brief discussion of why alternative embeddings (such as a co-rotating straight string) do not correspond to a quark at rest in the rotating frame and would generally describe different physical situations. This revision will not alter the reported results but will clarify the assumptions. revision: yes

  2. Referee: [§4 (Perturbative charged CCLP analysis)] The regularity condition on the Lorentzian worldsheet is invoked to fix the angular integration constants and obtain a finite renormalized transverse drag force. However, the manuscript does not provide an explicit check that the renormalized quantities remain cutoff-independent at the order considered or that the perturbative result matches the exact neutral-limit expression beyond leading order; without such verification the smoothness of the Kerr-AdS limit remains unconfirmed.

    Authors: We agree with the referee that an explicit verification of cutoff independence for the renormalized quantities and a direct matching to the exact neutral Kerr-AdS result would provide stronger confirmation of the perturbative analysis and the smooth limit. In the current manuscript, the Lorentzian worldsheet regularity condition is used to fix the integration constants, after which the transverse force is shown to be finite; however, the cutoff independence is implicit rather than demonstrated order-by-order, and the matching is only stated at leading order. To address this, we will add an appendix containing: (i) an explicit expansion of the renormalized drag force showing that all cutoff-dependent terms cancel at the perturbative order considered, and (ii) a term-by-term comparison of the slow-rotation expansion of the exact neutral Kerr-AdS drag force (from §3) with the neutral limit of the charged perturbative result, confirming agreement beyond leading order. These additions will confirm the smoothness of the Kerr-AdS limit without changing the main conclusions. revision: yes

Circularity Check

0 steps flagged

Direct computation of drag force from string embeddings in fixed geometry; no circular reduction

full rationale

The derivation consists of explicit calculations: the drag force is obtained by evaluating the string action or equations of motion for the principal Killing string embedding in the neutral Kerr-AdS limit, producing a tangential anisotropic force that reduces to viscous form only for equal spins as a derived property of the metric components. In the charged CCLP case, slow-rotation perturbation plus worldsheet regularity conditions fix integration constants to produce a finite renormalised transverse force with smooth limit. These are standard holographic computations in a prescribed background; the results are not defined in terms of themselves, no parameters are fitted to data and then relabeled as predictions, and no load-bearing self-citations or uniqueness theorems imported from prior author work are invoked to force the outcome. The chain is self-contained against the external black-hole geometry.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard AdS/CFT dictionary for drag forces, the existence of the CCLP solution in 5D gauged supergravity, and the validity of the principal Killing string embedding; no new free parameters are introduced beyond the background rotation and charge parameters already present in the geometry.

axioms (2)
  • domain assumption The principal Killing string embedding correctly represents the heavy quark worldline in the rotating black hole background.
    Invoked to obtain the exact drag force in the neutral limit.
  • domain assumption Worldsheet regularity in the Lorentzian signature fixes the angular integration constants unambiguously.
    Used to obtain the finite renormalised transverse drag in the charged case.

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