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arxiv: 2604.10163 · v1 · submitted 2026-04-11 · ✦ hep-th · cond-mat.str-el

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Hall transports from Taub-NUT AdS black holes

Mohd Aariyan Khan , Hemant Rathi , Dibakar Roychowdhury
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:58 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords Hall transportTaub-NUT AdS black holesframe-draggingholographic conductivityprobe D-branesMisner string
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The pith

Taub-NUT AdS black holes exhibit finite Hall transport due to frame-dragging from the NUT parameter.

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

The paper establishes that Taub-NUT AdS black holes in four dimensions yield finite Hall transport coefficients when analyzed through probe D-branes. The NUT parameter introduces a novel frame-dragging effect that modifies the holographic charge transport under constant electric and varying magnetic fields. This influence stands out in low-temperature regimes and near the Misner string for weak magnetic fields but vanishes under stronger magnetic fields. Readers would find this relevant as it links gravitational features like rotation to observable transport in strongly coupled quantum systems via holography.

Core claim

In the probe D-brane framework applied to Taub-NUT AdS black holes, the NUT parameter generates frame-dragging that produces finite Hall conductivity in the boundary theory. Calculations across low and high temperature regions, both near and far from the Misner string, indicate that these frame-dragging contributions to Hall transport are appreciable only at lower temperatures with small magnetic fields near the string, becoming insignificant at finite magnetic fields.

What carries the argument

Probe D-branes embedded in the Taub-NUT AdS geometry, with the NUT parameter serving as the source of frame-dragging that alters the response to external electric and magnetic fields.

If this is right

  • Frame-dragging produces a nonzero Hall conductivity.
  • The effect is pronounced at low temperatures and close to the Misner string under small magnetic fields.
  • Increasing the magnetic field to finite values suppresses the frame-dragging contribution to transport.
  • Separate analysis in low and high temperature limits reveals the temperature dependence of the conductivities.

Where Pith is reading between the lines

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

  • This frame-dragging mechanism might correspond to rotational effects in real materials that show Hall conductivity, suggesting holographic models for rotating condensed matter systems.
  • Similar studies in other NUT-charged geometries could uncover patterns in anomalous Hall transport across different dimensions.
  • Including the backreaction of the D-brane might lead to modifications in the bulk geometry that affect the transport coefficients further.

Load-bearing premise

The probe D-brane approximation remains valid, allowing the NUT parameter to map directly to frame-dragging in the dual field theory without notable backreaction or higher-order corrections.

What would settle it

Computing the Hall conductivity in this setup and finding it to be zero or independent of the NUT parameter at low temperatures near the Misner string with small magnetic field would disprove the presence of finite Hall transport from frame-dragging.

Figures

Figures reproduced from arXiv: 2604.10163 by Dibakar Roychowdhury, Hemant Rathi, Mohd Aariyan Khan.

Figure 1
Figure 1. Figure 1: σθϕ,U(1) vs temperature plot. Here we set E = 0.1, Jt = 10 and n = 0.2. Figures 1 and 2 show the behavior of U(1) Hall conductivity σθϕ,U(1), (which arise from the externally added U(1) charge carriers) and the thermal Hall conductivity 12 [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: σθϕ,thermal vs temperature plot. Here we set E = 0.1, Jt = 10 and n = 0.2. Next, we discuss the contribution due to thermally produced charge carriers to Hall conductivity. Notice that like the U(1) Hall conductivities, σθϕ,thermal (46)-(47) also increases as we move towards the threshold temperature, T ∼ Tmin, and the rise is particularly more significant near the Misner string. On the other hand, the con… view at source ↗
Figure 3
Figure 3. Figure 3: σϕϕ,U(1) vs temperature plot. Here, we set for E = 0.1 and Jt = 10. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: σϕϕ,thermal vs temperature plot. Here, we set E = 0.1 and Jt = 10. As before, both the externally added U(1) charge carriers and the thermally produced charge pairs are further drifted toward the Misner string due to frame dragging (43). This leads to the larger conductivities near Misner string as shown below σϕϕ,U(1) [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: σϕϕ vs temperature plot. Here, we set E = 0.1, Jt = 10, and n = 0.2. 2 4 6 8 10 T 0.95 1.00 1.05 1.10 σϕϕ,thermal β = 1 NM(θ = 0.1π) FM(θ=0.9π) (a) σϕϕ,U(1) vs temperature at B = 0.01 2 4 6 8 10 T 0.95 1.00 1.05 1.10 σϕϕ,thermal β = 1 NM(θ = 0.1π) FM(θ=0.9π) (b) σϕϕ,(U1) vs temperature at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: σϕϕ vs temperature plot. Here, we set E = 0.1, Jt = 10, and n = 0.2. In addition, at high temperatures, the number of thermally charged pairs ex￾ceeds that of U(1) charge carriers, leading to higher thermal Ohmic conductivity irrespective of the position of the Misner string, as shown in the ratio below. σϕϕ,thermal σϕϕ,U(1) [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: σθϕ,U(1) vs temperature plot. Here, we set E = 0.1, Jt = 10, and n = 0.2. 10When we are far from the Misner string, σθϕ,thermal (77) nearly vanishes, provided BEnT 4 min < T4 . 20 [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: σθϕ,thermal vs temperature plot. Here, we set E = 0.1, Jt = 10, and n = 0.2. It is worth noting that the contribution due to the U(1) charge carriers to the Hall conductivity dominates over the thermal contribution, even in the high temperature regime, as demonstrated below σ fM θϕ,U(1) σ fM θϕ,thermal >> 1 , σ nM θϕ,U(1) σ nM θϕ,thermal = Jt tan θ 2  2En csc θ >> 1. (79) This observation is in contrast w… view at source ↗
Figure 9
Figure 9. Figure 9: σθϕ vs temperature plot. Here we set E = 0.1, B = 10, Jt = 10 and n = 0.2 [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: σϕϕ vs temperature plot. Here, we set for E = 0.1, B = 10, and Jt = 10. The fact that frame-dragging effects are negligible at higher magnetic fields (and at lower temperatures) can be better understood by examining the ratio of Ohmic 25 [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: σϕϕ vs temperature plot. Here, we set for E = 0.1, B = 10, Jt = 10 and n = 0.2. σϕϕ,U(1) σϕϕ,thermal [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: σθϕ vs temperature plot. Here we set E = 0.1, Jt = 10 and n = 0.2. Finally, one can show that the Hall conductivity due to U(1) dominates over the thermal contribution, irrespective of the angular position of the Misner string (see [PITH_FULL_IMAGE:figures/full_fig_p030_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: σθϕ,U(1) vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. 0.30 0.35 0.40 0.45 0.50 T 0.005 0.010 0.015 0.020 σθϕ,thermal β = 0 Tmin NM(θ = 0.9π) FM(θ=0.45π) (a) σθϕ,thermal vs T at B = 0.01 0.30 0.35 0.40 0.45 0.50 T 0.02 0.04 0.06 0.08 0.10 0.12 σθϕ,thermal β = 0 Tmin NM(θ = 0.9π) FM(θ=0.45π) (b) σθϕ,thermal vs T at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p039_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: σθϕ,Thermal vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. 39 [PITH_FULL_IMAGE:figures/full_fig_p039_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: σϕϕ,U(1) vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. 0.30 0.35 0.40 0.45 0.50 T 1.0 1.1 1.2 1.3 1.4 σϕϕ,thermal β = 0 Tmin NM(θ = 0.9π) FM(θ=0.45π) (a) σϕϕ,Thermal vs T at B = 0.01 0.35 0.40 0.45 0.50 T 0.96 0.98 1.00 1.02 1.04 σϕϕ,thermal β = 0 Tmin NM(θ = 0.9π) FM(θ=0.45π) (b) σϕϕ,Thermal vs T at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p040_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: σϕϕ,Thermal vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. Like β = 1, both Hall and Ohmic conductivities due to U(1) carriers and ther￾mally produced charge pairs are higher near the Misner as compared to far from it, 40 [PITH_FULL_IMAGE:figures/full_fig_p040_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: σθϕ,U(1) vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. 0.30 0.35 0.40 0.45 0.50 T 0.01 0.02 0.03 0.04 0.05 σθϕ,thermal β = -1 Tmin NM(θ = 0.9π) FM(θ=0.1π) (a) σθϕ,thermal vs T at B = 0.01 0.30 0.35 0.40 0.45 0.50 T 0.05 0.10 0.15 0.20 σθϕ,thermal β = -1 Tmin NM(θ = 0.9π) FM(θ=0.1π) (b) σθϕ,thermal vs T at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p042_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: σθϕ,Thermal vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. 0.30 0.35 0.40 0.45 0.50 T 20 40 60 80 100 σϕϕ,U (1) β = -1 Tmin NM(θ = 0.9π) FM(θ = 0.1π) (a) σϕϕ,U(1) vs T at B = 0.01 0.30 0.35 0.40 0.45 0.50 T 10 20 30 40 σϕϕ,U (1) β = -1 Tmin NM(θ = 0.9π) FM(θ=0.1π) (b) σϕϕ,U(1) vs T at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p042_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: σϕϕ,U(1) vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. 42 [PITH_FULL_IMAGE:figures/full_fig_p042_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: σϕϕ,Thermal vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. Like previous examples with β = 1 and β = 0, both Hall and Ohmic conductiv￾ities due to U(1) carriers and thermally produced charge pairs are higher near the Misner string as compared to far from it, which is shown below. σθϕ,U(1) [PITH_FULL_IMAGE:figures/full_fig_p043_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: σϕϕ,U(1) vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. 44 [PITH_FULL_IMAGE:figures/full_fig_p044_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: σϕϕ,thermal vs temperature plot. Here, we set E = 0.1, Jt = 10 and n = 0.2. We can see from the above Figures (21 and 22) that Ohmic conductivity due to U(1) and thermal pairs are identical near far away from Misner string. The holographic Hall conductivity (σθϕ) (see Appendix B (140)-(141)) for β = 0 and in the high temperature regime take the following forms σθϕ,U(1) [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 23
Figure 23. Figure 23: σθϕ vs T plot for β = 0, E = 0.1 and Jt = 10 at small B. 45 [PITH_FULL_IMAGE:figures/full_fig_p045_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: σθϕ,thermal vs temperature plot. Here, we set E = 0.1, Jt = 10 and n = 0.2. Finally, we provide the expressions for Ohmic and Hall conductivity and their plots against temperature for β = −1 σϕϕ,U(1) [PITH_FULL_IMAGE:figures/full_fig_p046_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: σϕϕ,U(1) vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. 2 4 6 8 10 T 0.95 1.00 1.05 1.10 σϕϕ,thermal β =- 1 NM(θ = 0.9π) FM(θ=0.1π) (a) σϕϕ,thermal vs temperature at B = 0.01 2 4 6 8 10 T 0.95 1.00 1.05 1.10 σϕϕ,thermal β =- 1 NM(θ = 0.9π) FM(θ=0.1π) (b) σϕϕ,thermal vs temperature at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p047_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: σϕϕ,thermal vs temperature plot. Here, we set E = 0.1, Jt = 10 and n = 0.2. 2 4 6 8 10 T 0.00001 0.00002 0.00003 0.00004 0.00005 σθϕ,U (1) β = -1 NM(θ = 0.9π) FM(θ=0.1π) (a) σθϕ,U(1) vs T at B = 0.01 2 4 6 8 10 T 0.0001 0.0002 0.0003 0.0004 0.0005 σθϕ,U (1) β = -1 NM(θ = 0.9π) FM(θ=0.1π) (b) σθϕ,U(1) vs T at B = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p047_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: σθϕ vs T plot for β = −1, E = 0.1 and Jt = 10 at small B. 47 [PITH_FULL_IMAGE:figures/full_fig_p047_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: σθϕ,thermal vs temperature plot. Here, we set E = 0.1, Jt = 10 and n = 0.2. References [1] E. Witten, “Anti de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253-291 (1998) doi:10.4310/ATMP.1998.v2.n2.a2 [arXiv:hep-th/9802150 [hep￾th]]. [2] J. M. Maldacena, “The Large N limit of superconformal field the￾ories and supergravity,” Adv. Theor. Math. Phys. 2, 231-252 (1998) doi:10.4310/ATMP.1998.v2.n… view at source ↗
read the original abstract

We compute Hall transport coefficients associated with Taub-NUT AdS black holes in four space-time dimensions using the probe D-brane approach. In particular, we examine the effects due to the NUT parameter ($n$), or equivalently, the novel frame-dragging on the holographic charge transport properties. In our analysis, we treat the external electric field as a constant background, while varying the magnetic field ($B$) from small to finite. Within this framework, we analyze conductivities in both low and high temperature regions, focusing on locations that are both near and far from the Misner string. Our calculations show that frame-dragging effects are significant primarily at lower temperatures and near the Misner string, while a small magnetic field is maintained. However, these effects become negligibly small at a ``finite" magnetic field and even at lower temperatures. Our analysis reveals the existence of finite Hall transport, that has its origin in the novel frame-dragging.

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 manuscript computes Hall transport coefficients for 4D Taub-NUT AdS black holes via the probe D-brane DBI action on the fixed background geometry. It reports finite Hall conductivity arising from the NUT parameter n (equivalently, novel frame-dragging effects encoded in metric cross terms), which are prominent at low temperatures and near the Misner string for small magnetic field B, but become negligible at finite B even at low T. The analysis treats the electric field as a constant background and examines conductivities in low/high-T regimes both near and far from the Misner string.

Significance. If the probe approximation and attribution hold, the work supplies a holographic model in which off-diagonal Hall transport is generated purely by gravitational frame-dragging from the NUT charge, without external rotation or additional matter fields. This could furnish a controlled setting for studying transport in strongly coupled systems with analogous geometric effects and offers a concrete realization of the abstract claim that finite Hall conductivity originates in the n-dependent metric terms.

major comments (2)
  1. [Probe D-brane setup and Misner-string analysis] § on probe D-brane setup and Misner-string placement: the central claim that finite Hall conductivity is reliably extracted from the DBI action and attributable to frame-dragging requires the probe limit to remain valid precisely where the n-dependent cross terms are largest. No explicit check is provided that the induced world-volume curvature remains small compared with the D-brane tension scale, nor that back-reaction stays perturbative near the coordinate singularity; this undermines the interpretation of the computed conductivity as a dual transport coefficient.
  2. [Conductivity calculations] Conductivity extraction (likely §4 or §5): the manuscript states that the Hall conductivity is obtained from the background geometry and probe action, yet supplies neither the explicit off-diagonal component of the conductivity tensor nor its reduction to the n-dependent metric cross terms. Without the formula, the limit n→0, or a comparison to the known vanishing Hall conductivity in the absence of frame-dragging, the attribution of the finite result to the novel frame-dragging cannot be verified.
minor comments (2)
  1. [Abstract] The abstract asserts that calculations were performed across temperature and magnetic-field regimes but contains no explicit formulas, numerical values, or error estimates; adding at least the leading expression for the Hall conductivity would improve readability.
  2. [Introduction] Notation for the NUT parameter n and the magnetic field B should be introduced with a brief reminder of their relation to the metric components and the dual field-theory quantities.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the paper to incorporate clarifications and additional details that strengthen the presentation.

read point-by-point responses

  1. Referee: [Probe D-brane setup and Misner-string analysis] the central claim that finite Hall conductivity is reliably extracted from the DBI action and attributable to frame-dragging requires the probe limit to remain valid precisely where the n-dependent cross terms are largest. No explicit check is provided that the induced world-volume curvature remains small compared with the D-brane tension scale, nor that back-reaction stays perturbative near the coordinate singularity; this undermines the interpretation of the computed conductivity as a dual transport coefficient.

    Authors: We appreciate the referee highlighting the need for explicit validation of the probe approximation in the regimes where frame-dragging effects from the NUT parameter are strongest. The manuscript employs the standard probe limit in which the D-brane tension is taken large relative to background scales, with back-reaction neglected by construction. To address the concern directly, the revised version will include a dedicated paragraph providing order-of-magnitude estimates of the induced world-volume curvature near the Misner string (for the small-B, low-T regime considered) and confirming that it remains well below the tension scale, ensuring the approximation stays perturbative. This addition will support the reliability of the extracted conductivities as holographic transport coefficients. revision: yes

  2. Referee: [Conductivity calculations] the manuscript states that the Hall conductivity is obtained from the background geometry and probe action, yet supplies neither the explicit off-diagonal component of the conductivity tensor nor its reduction to the n-dependent metric cross terms. Without the formula, the limit n→0, or a comparison to the known vanishing Hall conductivity in the absence of frame-dragging, the attribution of the finite result to the novel frame-dragging cannot be verified.

    Authors: We thank the referee for noting this omission in explicit presentation. The revised manuscript will include the full derivation of the conductivity tensor from the DBI action, with the explicit off-diagonal Hall component σ_xy isolated and shown to arise directly from the n-dependent metric cross terms g_tφ. We will demonstrate analytically that σ_xy vanishes identically in the limit n → 0, recovering the expected zero Hall conductivity for standard AdS black holes without frame-dragging, and provide a brief comparison to the vanishing result in the literature for non-NUT cases. These additions will make the attribution to the novel gravitational frame-dragging fully transparent and verifiable. revision: yes

Circularity Check

0 steps flagged

No circularity: Hall conductivity computed directly from DBI action on fixed background

full rationale

The paper derives the Hall transport coefficients by solving the equations of motion obtained from the probe D-brane DBI action evaluated on the Taub-NUT AdS metric, with the NUT parameter n entering explicitly through the metric cross terms that produce frame-dragging. Conductivities are extracted from the resulting current responses to applied electric and magnetic fields without any parameter fitting to data, without renaming a known result, and without load-bearing self-citations that close the derivation. The calculation remains self-contained against the external holographic dictionary and the given background geometry.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the AdS/CFT dictionary, the validity of the probe-brane limit, and the identification of the NUT parameter with frame-dragging; no new entities are postulated.

free parameters (2)
  • NUT parameter n
    Physical parameter of the Taub-NUT solution varied in the analysis; not fitted but chosen to explore effects.
  • Magnetic field B
    External field varied from small to finite values; treated as input.
axioms (2)
  • domain assumption AdS/CFT correspondence maps bulk gravity to boundary field theory transport
    Invoked to interpret bulk conductivities as holographic charge transport.
  • domain assumption Probe D-brane approximation neglects backreaction on the geometry
    Standard in holographic transport calculations; stated implicitly by the method choice.

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discussion (0)

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Reference graph

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