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arxiv: 2603.28495 · v2 · submitted 2026-03-30 · ✦ hep-th

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Supersymmetry and Attractors in N = 4 Supergravity

Abhinava Bhattacharjee , Bindusar Sahoo
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Pith reviewed 2026-05-14 01:35 UTC · model grok-4.3

classification ✦ hep-th
keywords attractor mechanismN=4 supergravitydyonic black holessupersymmetry preservationextremal black holesconstant moduliPoincaré supergravity
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The pith

Extremal black holes in N=4 supergravity preserve one quarter of the supersymmetries for generic dyonic charges.

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

The paper examines the attractor mechanism for extremal spherically symmetric black holes in pure N=4 Poincaré supergravity through numerical methods. It focuses on constant moduli solutions and shows that for generic dyonic charges satisfying p squared q squared greater than the square of their dot product, these solutions preserve exactly one quarter of the total supersymmetries. A sympathetic reader would care because this links the charge configuration directly to the fraction of preserved supersymmetry and the fixed near-horizon geometry in a simple supergravity model.

Core claim

In pure N=4 Poincaré supergravity, numerical demonstration of the attractor mechanism for extremal spherically symmetric black holes shows that constant moduli solutions with generic dyonic charges satisfying p²q² > (p.q)² always preserve one quarter of the total supersymmetries.

What carries the argument

The attractor mechanism for constant moduli solutions, which fixes the scalar values at the horizon according to the charges and fixes the preserved supersymmetry fraction.

If this is right

  • The horizon values of the moduli are determined solely by the electric and magnetic charges.
  • The near-horizon geometry takes the form of a supersymmetric AdS2 times S2 space.
  • These black holes provide explicit examples of quarter-BPS states in N=4 supergravity.
  • The entropy is fixed by the attractor values independent of the asymptotic moduli.

Where Pith is reading between the lines

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

  • The same charge inequality may control supersymmetry fractions in other extended supergravities.
  • Analytic proofs of the one-quarter preservation could be constructed from the numerical evidence.
  • String theory embeddings of these solutions might yield microscopic state counts matching the macroscopic entropy.

Load-bearing premise

The numerical demonstration of the attractor mechanism for the chosen spherically symmetric solutions reliably captures the generic behavior even when restricted to constant moduli.

What would settle it

A specific dyonic charge configuration satisfying p²q² > (p.q)² where the numerical integration yields a different supersymmetry fraction, such as one half or none.

Figures

Figures reproduced from arXiv: 2603.28495 by Abhinava Bhattacharjee, Bindusar Sahoo.

Figure 1
Figure 1. Figure 1: FIG. 1: The attractor flow of [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The attractor flow of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The attractor flow of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

In this paper, we study the attractor mechanism for extremal, spherically symmetric black holes in pure N = 4 Poincar\'e supergravity, which we demonstrate numerically. We further study the supersymmetries preserved by these solutions by focussing specifically on the constant moduli solutions and show that, for a generic dyonic charge configuration satisfying $p^2q^2>(p.q)^2$, they always preserve 1/4th of the total supersymmetries.

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 / 1 minor

Summary. The manuscript studies the attractor mechanism for extremal spherically symmetric black holes in pure N=4 Poincaré supergravity, which is demonstrated numerically. It further examines the supersymmetries preserved by these solutions by restricting the analysis to constant-moduli solutions, concluding that for generic dyonic charge configurations satisfying p²q²>(p.q)² these solutions always preserve 1/4 of the total supersymmetries.

Significance. If the results hold, the work contributes numerical evidence for the attractor mechanism in N=4 supergravity and clarifies supersymmetry preservation for a class of dyonic solutions. The numerical demonstration of attractors for the chosen spherically symmetric ansätze is a positive element that could aid future analytic studies of moduli stabilization and black-hole entropy in extended supergravity.

major comments (1)
  1. [Supersymmetry preservation analysis (constant-moduli restriction)] The central claim that solutions 'always' preserve 1/4 SUSY for generic charges obeying p²q²>(p.q)² rests on restricting the supersymmetry analysis to the constant-moduli subclass. No argument is supplied showing that non-constant moduli flows (still satisfying the equations of motion and the same charge condition) cannot preserve a different fraction of Killing spinors. This restriction is load-bearing for the generality asserted in the abstract and conclusion.
minor comments (1)
  1. [Abstract and numerical section] The abstract states that the attractor mechanism is demonstrated numerically, yet the main text would benefit from explicit description of the numerical ansatz, integration method, and convergence criteria used for the spherically symmetric solutions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and will revise the manuscript accordingly to clarify the scope of our results.

read point-by-point responses

  1. Referee: [Supersymmetry preservation analysis (constant-moduli restriction)] The central claim that solutions 'always' preserve 1/4 SUSY for generic charges obeying p²q²>(p.q)² rests on restricting the supersymmetry analysis to the constant-moduli subclass. No argument is supplied showing that non-constant moduli flows (still satisfying the equations of motion and the same charge condition) cannot preserve a different fraction of Killing spinors. This restriction is load-bearing for the generality asserted in the abstract and conclusion.

    Authors: We agree that the supersymmetry analysis is restricted to constant-moduli solutions, as explicitly stated in the manuscript. No argument is given for non-constant moduli flows because the Killing spinor equations become substantially more involved with position-dependent scalars, and our numerical study focused on the constant case to confirm the attractor mechanism. We will revise the abstract and conclusion to state clearly that the 1/4 SUSY preservation result applies specifically to constant-moduli solutions satisfying the charge condition p²q²>(p.q)². We will also add a remark that the extension to non-constant flows remains open for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper numerically demonstrates the attractor mechanism for extremal spherically symmetric black holes in N=4 supergravity and then restricts the supersymmetry analysis to the constant-moduli subclass for dyonic charges satisfying p²q²>(p.q)², concluding 1/4 SUSY preservation. No derivation step reduces by construction to its inputs, no parameters are fitted and relabeled as predictions, and no self-citations or imported uniqueness theorems bear the central load. The numerical checks and subclass restriction are presented as explicit methodological choices rather than hidden equivalences, leaving the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information on free parameters, axioms, or invented entities is available from the abstract alone.

pith-pipeline@v0.9.0 · 5367 in / 1074 out tokens · 60227 ms · 2026-05-14T01:35:50.891337+00:00 · methodology

discussion (0)

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Reference graph

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