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arxiv: 2605.05178 · v1 · submitted 2026-05-06 · ✦ hep-th · gr-qc

On the generalized Komar charge of supersymmetric solutions

Tom\'as Ort\'in This is my paper

Pith reviewed 2026-05-08 17:32 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords generalized Komar chargessupersymmetric solutionsKilling spinorsBPS boundssupergravityN=2 d=4N=1 d=5N=1 d=10
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The pith

Generalized Komar charges vanish identically for supersymmetric Killing vectors built from Killing spinor bilinears in specified supergravity theories.

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

The paper shows that generalized Komar charges, computed for the supersymmetric Killing vector formed as a bilinear of Killing spinors, are identically zero in the supersymmetric solutions of certain supergravity theories. These theories are the ungauged N=2 supergravity in four dimensions, N=1 supergravity in five dimensions coupled to vector multiplets, and pure N=1 supergravity in ten dimensions. A reader would care because the vanishing supplies a coordinate-independent route to proving the BPS bounds that many of these solutions obey, linking the spinorial structure directly to conserved charges. The result applies specifically to solutions that admit such Killing spinors and holds without choosing special coordinates or frames.

Core claim

In the supersymmetric solutions of the considered supergravity theories, the generalized Komar charge evaluated on the supersymmetric Killing vector, constructed as the bilinear of the Killing spinors, vanishes identically. This vanishing property is established for the listed theories and provides a way to prove the supersymmetry bounds satisfied by some of those solutions in a rigorous manner that does not depend on coordinate choices.

What carries the argument

The generalized Komar charge evaluated on the supersymmetric Killing vector constructed as a bilinear of the Killing spinors.

If this is right

  • The vanishing supplies a coordinate-independent proof of BPS bounds for some of the solutions.
  • The result holds across the ungauged N=2 d=4, N=1 d=5 with vector multiplets, and pure N=1 d=10 supergravity theories.
  • The property ties the conserved charge directly to the existence of Killing spinors without additional assumptions on the metric or fields.

Where Pith is reading between the lines

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

  • The same vanishing might be checked in other supergravity theories with similar spinor structures to test broader applicability.
  • This approach could simplify mass and charge calculations for supersymmetric black holes by avoiding explicit integration over asymptotic surfaces.
  • It suggests that spinor bilinears may serve as a general tool for identifying which Killing vectors carry zero charge in extended gravity theories.

Load-bearing premise

The solutions admit Killing spinors whose bilinears define a Killing vector, and the theories are precisely the ungauged N=2 d=4, N=1 d=5 with vector multiplets, and pure N=1 d=10 cases considered.

What would settle it

An explicit computation of the generalized Komar charge for the bilinear Killing vector in one of the listed supergravity theories, using a known supersymmetric solution such as an extremal black hole, that yields a nonzero value.

read the original abstract

We consider the supersymmetric solutions of several supergravity theories (ungauged $\mathcal{N}=2,d=4$ and $\mathcal{N}=1,d=5$ supergravities coupled to vector supermultiplets and pure $\mathcal{N}=1,d=10$ supergravity) and show that their generalized Komar charges vanish identically for the supersymmetric Killing vector which is constructed as a bilinear of the Killing spinors of those solutions. This property can be used to prove the supersymmetry (``BPS'') bounds satisfied by some of those solutions in a rigorous, coordinate-independent way.

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 / 2 minor

Summary. The paper considers supersymmetric solutions of ungauged N=2 d=4 and N=1 d=5 supergravities coupled to vector multiplets, as well as pure N=1 d=10 supergravity. It shows that the generalized Komar charges vanish identically for the supersymmetric Killing vector constructed as a bilinear of the Killing spinors. This identity is then applied to prove the BPS bounds satisfied by some of these solutions in a rigorous, coordinate-independent way.

Significance. If the central identity holds, the result supplies a direct algebraic route to BPS bounds that avoids coordinate-dependent arguments and relies only on the Killing spinor equations together with the explicit form of the generalized Komar integrand. This is a clear strength for the field, as it furnishes an exact, non-numerical identity that can be checked against known solutions. No machine-checked proofs or reproducible code are provided, but the purely algebraic character of the claim is itself a positive feature.

major comments (1)
  1. [§3] §3, around Eq. (3.12): the cancellation that makes the generalized Komar charge vanish is stated to follow from the Killing spinor equation, but the intermediate algebraic steps that contract the bilinear with the curvature and flux terms are not shown explicitly. Without these steps the identity remains asserted rather than derived, which is load-bearing for the central claim.
minor comments (2)
  1. [Introduction] The abstract and introduction list the theories considered, but a short table summarizing the field content and the precise form of the generalized Komar integrand for each case would improve readability.
  2. [§4] In §4 the application to BPS bounds refers to 'some of those solutions' without naming which explicit solutions are used as checks; adding one or two concrete examples (e.g., the BMPV black hole or a simple 10d plane-wave) would make the utility of the identity clearer.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comment. We address the point raised below.

read point-by-point responses

  1. Referee: [§3] §3, around Eq. (3.12): the cancellation that makes the generalized Komar charge vanish is stated to follow from the Killing spinor equation, but the intermediate algebraic steps that contract the bilinear with the curvature and flux terms are not shown explicitly. Without these steps the identity remains asserted rather than derived, which is load-bearing for the central claim.

    Authors: We agree that the intermediate algebraic steps were not displayed explicitly. In the revised version we will expand the discussion around Eq. (3.12) by inserting the explicit contractions of the supersymmetric bilinear with the curvature and flux terms, showing term-by-term cancellation that follows directly from the Killing spinor equations. This will render the vanishing of the generalized Komar charge fully derived rather than asserted. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives an algebraic identity: generalized Komar charges vanish identically on the supersymmetric Killing vector built from Killing spinor bilinears, using the Killing spinor equations and the explicit form of the Komar integrand in the listed ungauged supergravity theories. This is presented as a direct calculation without reference to fitted parameters, self-referential definitions, or load-bearing self-citations that reduce the central claim to its inputs. The abstract and construction indicate a self-contained mathematical identity that can then be applied to BPS bounds, with no reduction by construction or smuggling of ansatze via citation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities are identifiable from the given information.

pith-pipeline@v0.9.0 · 5384 in / 1023 out tokens · 41923 ms · 2026-05-08T17:32:32.289350+00:00 · methodology

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Reference graph

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