An extremal black hole with a unique ground state

Swapnamay Mondal

arxiv: 2411.11096 · v1 · submitted 2024-11-17 · ✦ hep-th · gr-qc

An extremal black hole with a unique ground state

Swapnamay Mondal This is my paper

Pith reviewed 2026-05-23 08:37 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords extremalstateblackgrounddescriptionenergyholesnon-supersymmetric

0 comments

The pith

Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.

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

Extremal black holes sit at the edge of the allowed mass-charge relation. When supersymmetry is absent, string theory models them with four stacks of D-branes wrapping cycles on a six-torus and intersecting at one point. The authors write the low-energy worldline theory for this configuration. It contains 32 Goldstinos from completely broken supersymmetry and 28 Goldstones from broken translations. The resulting quantum Hamiltonian is then diagonalized. Its lowest-energy eigenstate is unique and has strictly positive energy, so no state sits exactly at the extremal bound.

Core claim

The Hamiltonian has a unique ground state, which carries a non-zero energy implying the absence of any truly extremal state.

Load-bearing premise

The low-energy worldline Lagrangian constructed from the four D-brane stacks with the stated orientations and intersection accurately captures the full dynamics without higher-order corrections or additional light modes that could alter the ground-state count.

read the original abstract

Recent computations in gravity suggest that non-supersymmetric extremal black holes lack any sizeable ground state degeneracy. We confirm this for D-brane description of non-supersymmetric 4-charge extremal black holes in N=8 string theory. The microscopic description comprises four stacks of D-branes wrapping various cycles of the internal six-torus and intersecting at a point. The orientations of the stacks are such that supersymmetry is broken completely. We construct the low energy worldline Lagrangian for the brane system, which is seen to have 32 Goldstinos and 28 Goldstones. The Hamiltonian has a unique ground state, which carries a non-zero energy implying the absence of any truly extremal state.

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

The paper builds a non-supersymmetric D-brane worldline model and claims its Hamiltonian has a unique positive-energy ground state, but the abstract supplies no equations to check the steps.

read the letter

This paper takes four D-brane stacks on T^6 with orientations that break all supersymmetry and constructs the low-energy 0+1d Lagrangian for the intersection. It counts 32 Goldstinos and 28 Goldstones, then states that the resulting Hamiltonian has a single ground state carrying positive energy. That is the central claim, and it lines up with the gravity-side hints that non-BPS extremal holes lack large degeneracy. The construction itself follows the usual intersecting-brane rules, so the setup is standard for this subfield. What is new is the explicit application to a fully non-supersymmetric 4-charge configuration and the direct ground-state statement for that case. The paper therefore gives a concrete microscopic example rather than another general argument. The main soft spot is the absence of any displayed Lagrangian, Hamiltonian, or diagonalization steps in the abstract. Without those, it is impossible to see how uniqueness and positive energy were established or whether all relevant operators were kept. The stress-test concern about missing higher-order terms or extra light modes is therefore still open; if the full text only asserts the result without a reproducible calculation, the conclusion does not yet follow. The work is aimed at people who count microstates for non-BPS black holes in string theory. A reader already familiar with D-brane effective actions will understand the setup quickly and can judge whether the ground-state claim holds once the equations appear. It is worth sending to peer review because the question is current and the model is specific enough that referees can check the algebra directly. If the Hamiltonian analysis is written out clearly, the paper can be revised; if the steps remain opaque, that will become clear in review.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that non-supersymmetric 4-charge extremal black holes in N=8 string theory, realized microscopically by four D-brane stacks with orientations that break all supersymmetry, admit a low-energy worldline Lagrangian containing 32 Goldstinos and 28 Goldstones. The associated Hamiltonian is asserted to possess a unique ground state carrying strictly positive energy, implying the absence of any truly extremal (zero-energy) state and thereby confirming recent gravity-based indications of vanishing ground-state degeneracy.

Significance. If the Hamiltonian analysis holds, the result supplies a concrete microscopic confirmation, using standard D-brane constructions without fitted parameters, of the absence of degeneracy for non-supersymmetric extremal black holes. This strengthens the broader program linking gravity computations to string-theory microstate counting and provides a falsifiable prediction that the effective 0+1-dimensional theory has no zero-energy vacuum.

major comments (2)

[Abstract / low-energy worldline Lagrangian construction] The central claim rests on the assertion that the constructed worldline Lagrangian encodes precisely the 32 Goldstinos + 28 Goldstones with no additional light modes or relevant higher-order operators that could lift or degenerate the ground state. No explicit form of the Lagrangian, interaction terms, or derivation of the mode count is supplied, so it is impossible to verify that the truncation is reliable at the scale set by the brane charges (see the skeptic's weakest assumption).
[Abstract / Hamiltonian analysis] The statement that 'the Hamiltonian has a unique ground state' with E > 0 is load-bearing for the conclusion that no truly extremal state exists, yet no explicit Hamiltonian, spectrum computation, or uniqueness proof is provided. Without these steps the claim cannot be checked and the link to the gravity computations remains unverified.

minor comments (1)

[Abstract] The abstract is unusually dense and would benefit from a single sentence clarifying the four brane stacks and their wrapping cycles before stating the Goldstino/Goldstone count.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the low-energy worldline theory for the chosen D-brane orientations correctly encodes the full spectrum of light modes and that the resulting Hamiltonian is the correct effective description.

axioms (1)

domain assumption The low-energy effective theory of the four intersecting D-brane stacks is given by a worldline Lagrangian containing exactly 32 Goldstinos and 28 Goldstones.
Invoked in the abstract as the starting point for the Hamiltonian analysis.

pith-pipeline@v0.9.0 · 5636 in / 1201 out tokens · 26019 ms · 2026-05-23T08:37:03.213487+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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D. N. Page, Thermodynamics of near extreme black holes , 9, 2000. hep-th/0012020

work page internal anchor Pith review Pith/arXiv arXiv 2000

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Preskill, P

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work page internal anchor Pith review Pith/arXiv arXiv 2016

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work page internal anchor Pith review Pith/arXiv arXiv 2019

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Choi and F

S. Choi and F. Larsen, AdS2 Holography and Eﬀective QFT , 2302.13917

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Ghosh, H

A. Ghosh, H. Maxﬁeld and G. J. Turiaci, A universal Schwarzian sector in two-dimensional conformal ﬁeld theories , JHEP 05 (2020) 104, [ 1912.07654]

work page arXiv 2020

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Mondal, Statistical Mechanics of Exponentially Many Low Lying State s, 2310.12264

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work page arXiv

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Microscopic Origin of the Bekenstein-Hawking Entropy

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work page internal anchor Pith review Pith/arXiv arXiv 1996

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J. M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M theory , JHEP 12 (1997) 002, [ hep-th/9711053]

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J. C. Breckenridge, D. A. Lowe, R. C. Myers, A. W. Peet, A. Strominger and C. Vafa, Macroscopic and microscopic entropy of near extremal spinn ing black holes , Phys. Lett. B 381 (1996) 423–426, [ hep-th/9603078]

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J. M. Maldacena, D-branes and near extremal black holes at low-energies , Phys. Rev. D 55 (1997) 7645–7650, [ hep-th/9611125]

work page internal anchor Pith review Pith/arXiv arXiv 1997

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G. T. Horowitz, J. M. Maldacena and A. Strominger, Nonextremal black hole microstates and U duality , Phys. Lett. B 383 (1996) 151–159, [ hep-th/9603109]. – 12 –

work page internal anchor Pith review Pith/arXiv arXiv 1996

[26] [26]

Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes

K. Sfetsos and K. Skenderis, Microscopic derivation of the Bekenstein-Hawking entropy formula for nonextremal black holes , Nucl. Phys. B 517 (1998) 179–204, [ hep-th/9711138]

work page internal anchor Pith review Pith/arXiv arXiv 1998

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J. M. Maldacena, Probing near extremal black holes with D-branes , Phys. Rev. D 57 (1998) 3736–3741, [ hep-th/9705053]

work page internal anchor Pith review Pith/arXiv arXiv 1998

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J. M. Maldacena, Statistical entropy of near extremal ﬁve-branes , Nucl. Phys. B 477 (1996) 168–174, [ hep-th/9605016]

work page internal anchor Pith review Pith/arXiv arXiv 1996

[29] [29]

G. T. Horowitz, D. A. Lowe and J. M. Maldacena, Statistical entropy of nonextremal four-dimensional black holes and U duality , Phys. Rev. Lett. 77 (1996) 430–433, [hep-th/9603195]

work page internal anchor Pith review Pith/arXiv arXiv 1996

[30] [30]

Microstates of Non-supersymmetric Black Holes

A. Dabholkar, Microstates of nonsupersymmetric black holes , Phys. Lett. B 402 (1997) 53–58, [hep-th/9702050]

work page internal anchor Pith review Pith/arXiv arXiv 1997

[31] [31]

U. H. Danielsson, A. Guijosa and M. Kruczenski, Brane anti-brane systems at ﬁnite temperature and the entropy of black branes , JHEP 09 (2001) 011, [ hep-th/0106201]

work page internal anchor Pith review Pith/arXiv arXiv 2001

[32] [32]

Near-BPS-Saturated Rotating Electrically Charged Black Holes as String States

M. Cvetic and D. Youm, Near BPS saturated rotating electrically charged black hol es as string states, Nucl. Phys. B 477 (1996) 449–464, [ hep-th/9605051]

work page internal anchor Pith review Pith/arXiv arXiv 1996

[33] [33]

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