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arxiv: 2604.18692 · v1 · submitted 2026-04-20 · ✦ hep-th

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Non-supersymmetric heterotic strings on AdS₄times S³times S³

Ivano Basile , Daniel Robbins , Hassaan Saleem
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:54 UTC · model grok-4.3

classification ✦ hep-th
keywords non-supersymmetric heterotic stringAdS flux compactificationsbrane nucleationtachyonic instabilitiesscale separationorbifold projectionsstability analysisnon-perturbative decay
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The pith

Non-supersymmetric heterotic AdS compactifications with two fluxes always decay via brane nucleation that equalizes them until tachyons appear.

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

The paper examines stability in a family of anti-de Sitter flux compactifications of the tachyon-free non-supersymmetric heterotic string. These solutions contain two independent unbounded fluxes threading the internal three-spheres. When the fluxes differ greatly, the geometry shows inverse scale separation with no tachyons in the spectrum. Brane nucleation always supplies a non-perturbative decay channel that reduces the difference between the fluxes. As the fluxes approach equality, tachyonic modes develop, although an orbifold projection can remove them.

Core claim

In this family of AdS4 × S3 × S3 flux compactifications, two independent unbounded fluxes control the geometry. When the fluxes are far apart, no tachyons appear and inverse scale separation occurs. When close, tachyons develop but can be orbifolded out. Non-perturbative brane nucleation instabilities are always present and drive the fluxes toward each other, eventually triggering tachyonic decay.

What carries the argument

The pair of independent unbounded fluxes threading the internal spheres, which set the scale separation and induce instabilities as their magnitudes approach each other.

Load-bearing premise

The family of anti-de Sitter flux compactifications with two independent unbounded fluxes exists and admits a reliable perturbative and non-perturbative stability analysis within the tachyon-free non-supersymmetric heterotic string.

What would settle it

An explicit computation showing that brane nucleation rates do not reduce the difference between the two fluxes, or that tachyonic modes fail to appear when the fluxes are equalized, would falsify the instability mechanism.

Figures

Figures reproduced from arXiv: 2604.18692 by Daniel Robbins, Hassaan Saleem, Ivano Basile.

Figure 1
Figure 1. Figure 1: Plots of L against log n for different values of ne given in the legend and vice versa. 2 3 4 5 6 7 8 Log10 n 20 40 60 80 L  α′ L  versus n 2 3 4 5 6 7 8 Log10 n  500 1000 1500 2000 2500 L  α′ L  versus n  [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plots of eL against log n for different values of ne given in the legend and vice versa. 4 Perturbative stability analysis 4.1 Background solution The ten dimensional effective action for O(16) × O(16) with one-loop corrected potential (in string frame) is S = 1 2κ 2 10 Z d 10 x p −g  e −2φ  R + 4(∂ φ) 2 − 1 12 |H3 | 2 ‹ − 2λg 2 s α′  . (23) This action results in the following equations of motion for t… view at source ↗
Figure 3
Figure 3. Figure 3: Plots of gs against log n for different values of ne given in the legend and vice versa. 2 3 4 5 6 7 8 Log10 n -0.035 -0.030 -0.025 -0.020 -0.015 -0.010 -0.005 α′ Vmin Vmin versus n 2 3 4 5 6 7 8 Log10 n  -0.035 -0.030 -0.025 -0.020 -0.015 -0.010 -0.005 α′ Vmin Vmin versus n  [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plots of Vmin against log n for different values of ne given in the legend and vice versa. ansatz means that the non-vanishing components of the ten-dimensional Riemann tensor are Rµνρσ = − L −2 A [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Plots of LA against log n for different values of ne given in the legend and vice versa. There is an overall scaling symmetry in the equations that determine the radii and the string coupling. To see this, let us write n 2 = x(1 + y), ne 2 = x(1 − y), (37) where we have introduced two new variables, x = n 2 + ne 2 2 , y = n 2 − ne 2 n2 + ne2 = 1 − ne 2 n2 1 + ne2 n2 . (38) In other words, x is the average … view at source ↗
Figure 6
Figure 6. Figure 6: The plot of L 2 Am2 − with m2 − coming from (179) for ℓ = eℓ = 1 and ± ′ = ∓ (orange) that violates the BF bound (blue) against log(n/ne). and it is below the scalar BF bound which can be written as m 2 BF = − 9 4 L −2 A = − 3 8 Λ = −0.375Λ. (181) Numerical analysis indicates that the BF bound is violated by this mode if 0.214 ≲ |n/n˜| ≲ 4.674. The mass squared with ℓ = eℓ = 1 and ± = ∓ ′ is plotted in [P… view at source ↗
Figure 7
Figure 7. Figure 7: The plots of six eigenvalues of the mass matrices for the [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The plots of the five eigenvalues for the mass matrix for the [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The plots of the eigenvalues for the mass matrix for the [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The plots of the eigenvalues for the mass matrices for the [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The plots of the eigenvalues for the mass matrices for the [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Plot of the extremality parameter βmax extremized over wrapping cycles as a function of the direction in flux space. One can observe that the decay process becomes fast when a hierarchy between fluxes is present. The minimal value, at￾tained only for n = ne, is p 5/3. 6 Discussion and outlook In this paper we carried on the search for (meta)stable non-supersymmetric solutions of string theory. Specificall… view at source ↗
read the original abstract

We analyze the stability properties of a family of anti-de Sitter flux compactifications of the tachyon-free non-supersymmetric heterotic string in ten dimensions. In contrast with simpler such solutions, the solutions include two independent unbounded fluxes, leading to richer instability phenomena. In particular, when the two fluxes are sufficiently close in magnitude, the perturbative spectrum develops tachyonic modes, which can be projected out by an orbifold action. When the fluxes are far apart, tachyonic modes are absent, and the geometry displays inverse scale separation, where a factor of the internal manifold becomes parametrically larger than the anti-de Sitter factor. Still, non-perturbative instabilities in the form of brane nucleation are always available decay channels, and tend to drive the two fluxes closer together, eventually triggering the tachyonic instability when present.

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 analyzes the perturbative and non-perturbative stability of a family of AdS4 × S3 × S3 flux compactifications in the tachyon-free non-supersymmetric heterotic string, featuring two independent unbounded fluxes. When the fluxes are close in magnitude, tachyonic modes appear in the spectrum and can be removed by an orbifold projection; when far apart, the geometry exhibits inverse scale separation without tachyons, but brane nucleation instabilities are claimed to be always present and to drive the fluxes closer together until tachyons are triggered.

Significance. If the central claims hold, the work provides a concrete example of how non-perturbative decay channels in multi-flux non-supersymmetric heterotic compactifications can destabilize geometries that appear stable at the perturbative level, reinforcing swampland expectations against stable non-SUSY AdS vacua. The inverse scale separation regime and the orbifold projection of tachyons are technically interesting features that could inform broader searches for controlled non-supersymmetric string vacua.

major comments (2)
  1. [§5] §5 (non-perturbative instabilities): the assertion that brane nucleation 'tend[s] to drive the two fluxes closer together' is load-bearing for the conclusion that far-apart regimes eventually trigger tachyons, yet no explicit instanton action is computed for the distinct channels (NS5-branes wrapping one S3 versus both S3 factors). Without comparing the Euclidean actions or deriving an effective potential on the (Q1, Q2) plane, it remains unclear why the dominant decay reduces |Q1 − Q2| rather than decreasing both fluxes proportionally or increasing their difference.
  2. [§3] §3 (perturbative spectrum): while the appearance of tachyons for close fluxes is stated, the manuscript does not provide the explicit mass-squared formula or the dependence on the flux ratio that would allow independent verification of the critical separation at which tachyons disappear.
minor comments (2)
  1. [Introduction] The definition of inverse scale separation (a factor of the internal manifold becoming parametrically larger than the AdS radius) should be stated quantitatively with the relevant flux scalings in the text, not only in the abstract.
  2. [§2] Notation for the two fluxes (Q1, Q2) and the orbifold action should be introduced consistently in §2 before being used in the stability analysis.

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 indicate the changes we will make in the revised version.

read point-by-point responses

  1. Referee: [§5] §5 (non-perturbative instabilities): the assertion that brane nucleation 'tend[s] to drive the two fluxes closer together' is load-bearing for the conclusion that far-apart regimes eventually trigger tachyons, yet no explicit instanton action is computed for the distinct channels (NS5-branes wrapping one S3 versus both S3 factors). Without comparing the Euclidean actions or deriving an effective potential on the (Q1, Q2) plane, it remains unclear why the dominant decay reduces |Q1 − Q2| rather than decreasing both fluxes proportionally or increasing their difference.

    Authors: We agree that the non-perturbative analysis would benefit from a more explicit treatment. In the revised manuscript we will compute the Euclidean actions for the two distinct NS5-brane nucleation channels (wrapping a single S^3 versus wrapping both S^3 factors) and compare them as functions of the flux quanta Q1 and Q2. We will show that, for |Q1 − Q2| large, the channel that reduces the larger flux has the lower action and therefore dominates, driving the system toward equal fluxes. A qualitative sketch of the resulting effective potential on the (Q1, Q2) plane will also be added to illustrate the flow. revision: yes

  2. Referee: [§3] §3 (perturbative spectrum): while the appearance of tachyons for close fluxes is stated, the manuscript does not provide the explicit mass-squared formula or the dependence on the flux ratio that would allow independent verification of the critical separation at which tachyons disappear.

    Authors: We thank the referee for noting this omission. Although the spectrum analysis in §3 determines the existence of tachyons when the fluxes are close, the explicit mass-squared formula and its dependence on the flux ratio were not written out. In the revised version we will derive and display the mass-squared expression for the potentially tachyonic modes, state its dependence on the flux ratio, and indicate the critical value at which the tachyon mass squared changes sign. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper analyzes stability of AdS flux compactifications via perturbative spectrum (tachyons when fluxes close) and standard non-perturbative brane nucleation channels. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described claims. The statements on flux-driving instabilities follow from external spectrum calculations and instanton considerations rather than reducing to inputs by construction. The derivation remains self-contained against standard string theory benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of the described family of flux compactifications and the applicability of perturbative spectrum analysis plus brane nucleation in the non-supersymmetric heterotic string; no explicit free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption The non-supersymmetric heterotic string in ten dimensions is tachyon-free.
    Explicitly stated as the starting point for the compactifications analyzed.

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discussion (0)

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Reference graph

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