{"id":"3debb007-9ea3-4189-97a0-bd2f8d0bd0cc","arxiv_id":"2507.00615","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Numerical scans of Type IIB compactifications find single scalar potentials containing coexisting KKLT/LVS and Kahler-uplifted/LVS minima, including AdS, Minkowski, and dS pairs.","lead":"The paper numerically scans over 80,000 Calabi-Yau compactifications and finds single scalar potentials that contain two different metastable vacua at once, such as a small-volume KKLT minimum next to a large-volume LVS minimum. This gives string theorists a concrete setting to study vacuum decay inside one flux configuration rather than only between different flux choices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Coexistence is solid at EFT level, but the 'single flux configuration' requires an explicit flux realisation of the scanned (W0, gs, eKcs) point, which the paper does not provide.","rationale":"The reader's weakest assumption identifies rigid-divisor support for all h^{1,1} non-perturbative terms, and I agree that this is part of the gap. My concern is slightly broader: even with rigid divisors, the scanned values of W0, gs, and e^{Kcs} must be realised by an actual flux choice for the phrase 'single flux configuration' to be literally true. The paper's own caveats in §2.1 and footnote 10 admit this gap. This does not undermine the credible EFT-level numerics: Hessian checks are reported, known KKLT/LVS/Kähler-uplifted solutions are reproduced, and the dS condition of [60] is independently matched in Fig. 9. The coexistence phenomenon is therefore a well-supported property of a plausible effective potential, but the central string-realisation claim remains conditional on the existence of a flux vacuum at the scanned parameter point. Since the reader already issued a CONDITIONAL verdict on essentially these grounds, no verdict adjustment is needed.","tokens_in":26461,"tokens_out":6931,"duration_ms":89663,"concrete_test":"Use CYTools/JAXVacua (or an independent flux scan) on P4[1,1,1,6,9][18] to search for complex-structure flux vacua satisfying DτW = DzW = 0 with W0 and e^{Kcs} equal to the Fig. 11 values at gs = 0.055, and verify that both 4-cycles are rigid or can be rigidified by suitable gauge flux. If such a flux point exists within the D3-tadpole bound, rerun the Fig. 11 minimisation with the flux-determined W0 and e^{Kcs} and check that both minima persist. If no such flux point is found, the coexistence claim should be reported as an EFT-level result rather than a realised single-flux vacuum.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the coexisting vacua belong to a single flux configuration, but the paper never constructs or identifies the corresponding 3-form flux data. In §4.4 and §4.5, W0, gs, e^{Kcs}, Ai, ai, and alpha are scanned as independent inputs for a fixed Calabi-Yau, while §2.1 explicitly assumes complex-structure and dilaton stabilisation rather than performing it. Footnote 10 in §4.1 likewise concedes that the required non-perturbative contribution of all h^{1,1} divisors is not verified for small h^{1,1}. Thus the coexistence of the KKLT and LVS minima in Fig. 11 is a property of an assumed effective potential, not yet of a demonstrated Type IIB flux compactification. If no flux choice on P4[1,1,1,6,9][18] realises the values W0 ≈ -0.024, gs ≈ 0.055, e^{Kcs} ≈ 0.03 with rigid or rigidifiable divisors supporting ai = {2π/24, 2π/22}, then the strongest claim is not realised as stated. The EFT-level numerical evidence is credible and well validated; the missing link is UV realizability of the exact parameter point.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a JAX-based numerical framework, using automatic differentiation and just-in-time compilation, to compute and minimise the Type IIB Kähler-moduli scalar potential. The potential includes the BBHL alpha-prime correction, a logarithmic volume correction, non-perturbative superpotential terms, and optionally an anti-D3 uplift term. The authors scan Calabi-Yau orientifolds with h^{1,1} ≤ 6 from the Kreuzer-Skarke database, over ranges of the flux superpotential W0 and string coupling gs, and report reproduction of KKLT, LVS, Kähler-uplifted, and LVS-like hybrid vacua. The principal new claim is that a single scalar potential, for fixed UV parameters, can contain two local minima of different types (e.g., KKLT+LVS or Kähler-uplifted+LVS), and that upon adding an explicit uplift term one can realise all combinations of AdS, Minkowski, and dS vacua. The paper proposes these configurations as a novel setting for vacuum transitions within a fixed flux configuration.","tokens_in":26778,"tokens_out":8560,"duration_ms":94329,"significance":"If fully established, the coexistence result is a valuable step: previous analyses of transitions between string vacua mostly involved distinct flux choices or decay to decompactification, whereas here two metastable minima coexist in a single effective potential. The EFT-level numerical work is largely credible: minima are checked for Hessian positivity and Kähler-cone membership, and the recovered scaling relations (e.g., LVS τ_s ~ a_s^{-1} ln V, τ_b ~ V^{2/3}; KKLT volume vs |W0|) match analytic expectations. The framework's modularity and use of automatic differentiation are genuine technical assets. However, the headline interpretation as 'coexisting vacua in a single flux configuration' is not yet supported, because the UV parameters (W0, gs, e^{K_cs}, Ai, ai, alpha, D_up) are scanned inputs rather than derived from explicit 3-form flux data; this is acknowledged in part by §2.1 and footnote 10. The significance is therefore conditional on the missing flux realisation.","major_comments":[{"comment":"The paper's central claim that the coexisting minima belong to 'a single flux configuration' is not yet demonstrated. In Fig. 11 and throughout §4.4, the parameters W0, gs, e^{K_cs}, Ai, ai and alpha are scanned as independent inputs, while §2.1 states that complex-structure and dilaton stabilisation is assumed, not performed. No explicit choice of 3-form fluxes is constructed that yields the required values (e.g., W0 ≈ -0.024, gs ≈ 0.055, e^{K_cs} ≈ 0.03 for the left panel of Fig. 11) on P4[1,1,1,6,9][18] or any other Calabi-Yau, nor is the D3-tadpole constraint checked for such a point. Consequently, the coexisting minima are demonstrated properties of an assumed effective potential, not of a demonstrated Type IIB flux compactification. The authors should either provide a concrete flux realisation (or a parametric argument that flux choices in the required range exist) or state clearly in the abstract and conclusions that the results apply to the EFT at scanned parameter values.","section":"§4.4 (with §2.1)"},{"comment":"The analysis assumes that all h^{1,1} Kähler moduli contribute non-perturbatively to the superpotential (2.12), i.e., each corresponding 4-cycle is rigid or can be rigidified. Footnote 10 concedes that this has not been verified for small h^{1,1}. The featured coexistence examples use P4[1,1,1,6,9][18] with h^{1,1}=2 (Figs. 11-15); if either of these two divisor classes cannot support ED3 instantons or gaugino condensation, the non-perturbative superpotential would contain only one exponential term and the KKLT-LVS coexistence shown in these figures would not occur in the stated form. The authors should verify rigidity/rigidifiability for the specific geometries used in the headline examples, or restrict the claim accordingly.","section":"§4.1, footnote 10"},{"comment":"The uplift term V_up = D_up / V^{4/3} is introduced in Eq. (4.17) with D_up left as a free parameter; no computation of D_up from an explicit anti-D3-brane construction or alternative uplift is provided, and consistency with the D3-tadpole and warping constraints (see refs. [68-72]) is not checked. Since the claim that 'all combinations of AdS, Minkowski, and dS vacua' can be realised in a single potential depends directly on scanning D_up, the uplifted multi-vacuum configurations remain an EFT-level demonstration. A consistency check or an explicit construction for at least one D_up value would be needed to support the abstract's wording about de Sitter vacua in explicit flux compactifications.","section":"§4.5, Eq. (4.17)"}],"minor_comments":[{"comment":"The validation description says minima are checked for Hessian positivity and Kähler-cone membership; it would be useful to state how the Hessian is computed (e.g., via automatic differentiation) and how near-zero eigenvalues are treated numerically, particularly in flat directions.","section":"§3.3"},{"comment":"The sentence 'As described in §4.2 and §4.2' presumably should refer to §4.2 and §4.4; please correct the cross-reference.","section":"§4.5"},{"comment":"The phrase 'we can seen in the second plot' should read 'we can see in the second plot'.","section":"Fig. 13 caption"},{"comment":"The bullet 'Not bubble of nothing decay' is grammatically unclear; 'No bubble-of-nothing decay' would be clearer.","section":"§5.2"},{"comment":"The decay-rate formula for dS-to-Minkowski tunnelling involves S(phi0)/(1+(4V0/3 sigma^2)^2); the form is not immediately recognisable from standard Coleman-De Luccia expressions, and the stated sign flip for Minkowski-to-AdS decay deserves a derivation or a reference.","section":"Eq. (5.2)"}],"recommendation":"major_revision","confidential_remarks":"The reader's report and my own assessment agree on the main gap: the paper is a competent and technically solid EFT-level numerical study, but the abstract and conclusions overstate the UV-complete status of the coexisting-vacua claim. I would advise the editor that a major revision is appropriate, one that either supplies a concrete flux realisation for at least the featured example or carefully rewrites the claims to distinguish EFT-level results from demonstrated Type IIB flux compactifications. The numerical framework itself, and the cataloguing of coexisting minima at the EFT level, are worth publishing after such a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper is worth a serious referee. The JAX framework is a real step forward for numerical moduli stabilisation, and the coexistence of KKLT/LVS and Kähler-uplifted/LVS minima in one potential is a genuine new-in-this-form result. The authors are honest about what is assumed and what is not.\n\nWhat it does well: the pipeline (auto-diff, Hessian positivity, Kähler-cone checks) is validated by reproducing the known KKLT, LVS, and Kähler-uplifted solutions, including the Rummel-Westphal dS trajectory with fixed literature parameters. The scaling relations (τs ~ 1/a ln V, τb ~ V^{2/3}) match. The survey over 80,000 geometries at h^{1,1}≤6 is a real resource, even if the shallow scan mainly guides targeted searches. The coexistence claim is demonstrated with explicit potentials and parameter regions, not just anecdote. The authors also credit earlier work ([11] already saw multiple solutions for one parameter set; [13] had hybrid minima) rather than overclaiming novelty.\n\nSoft spots, in proportion. The main one is the gap between 'coexisting vacua in a scalar potential' and 'coexisting vacua in a single flux compactification.' W0, gs, e^{Kcs}, and the Ai are scanned inputs; the paper explicitly assumes complex-structure and dilaton stabilisation rather than performing it. No 3-form flux data is produced that realises the specific (W0, gs, e^{Kcs}) point used in the key figures. Footnote 10 concedes the all-divisors-rigid assumption is not verified at small h^{1,1}. So the central claim as stated is not yet backed by a demonstrated flux choice. That is a real limitation, though it does not undercut the EFT-level result: coexistence exists in the assumed effective potential, and the authors could reasonably reframe the claim.\n\nTwo smaller caveats. The logarithmic correction (2.15) is explicitly unproven, and α is a free parameter. And some of the interesting small-volume Kähler-uplifted vacua have δV/V ~ 0.5, i.e. outside perturbative control; the authors say so themselves. Neither is fatal, but together they mean the strongest 'all combinations of AdS/Minkowski/dS' statements should be read as statements about the ansatz, not about controlled string vacua. No code is released, which limits reproducibility; the framework is described clearly enough that this is fixable.\n\nWho this is for: anyone working on Type IIB moduli stabilisation or vacuum transitions should read at least §4 and §5. I agree with the reader's conditional verdict. My recommendation: send it to peer review, ask the authors to provide a flux realisation or soften the 'single flux configuration' language, verify rigid divisors for the showcased manifolds, and release the code.","headline":"A solid, honest numerical study that discovers coexisting moduli vacua at EFT level; the 'single flux configuration' framing needs UV input to be fully earned.","tokens_in":27316,"tokens_out":3688,"would_cite":true,"duration_ms":38901,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A fixed flux configuration can support two different metastable vacua, so vacuum tunnelling can occur without changing the fluxes.","keywords":["Type IIB flux compactifications","Kähler moduli stabilisation","KKLT minima","Large Volume Scenario","coexisting vacua","de Sitter vacua","Calabi-Yau orientifolds","vacuum tunnelling"],"falsifier":"Recompute the potential (2.16) for $\\mathbb{P}^4[1,1,1,6,9][18]$ with the same $g_s$, $W_0$, and $\\alpha$ but with the non-perturbative term for the large four-cycle removed; if both minima no longer coexist, the claim rests entirely on that cycle's rigidity. A direct check of whether that divisor has deformation modes that cannot be lifted by allowed worldvolume fluxes would settle the assumption.","tokens_in":26217,"feed_emoji":"🌌","tokens_out":12042,"duration_ms":130559,"temperature":0.7,"pith_summary":"This paper aims to show that a single, fixed choice of fluxes and background parameters in Type IIB string compactifications can support more than one metastable vacuum for the Kähler moduli. Using a fast numerical pipeline across more than 80,000 Calabi-Yau threefolds with up to six Kähler moduli, the authors reproduce the three established stabilisation scenarios — small-volume KKLT, large-volume LVS, and Kähler uplift — and identify parameter regions where two of them coexist in the same scalar potential. After adding an explicit anti-D3-brane uplift term, the coexisting pair can be tuned into any combination of AdS, Minkowski, and de Sitter minima. If correct, this means vacuum decay between different cosmological-constant vacua can be studied within one flux configuration, without invoking transitions between different flux choices.","feed_headline":"One set of string-theory fluxes can host two different vacua","feed_subtitle":"A scan of 80,000 Calabi-Yau spaces finds small- and large-volume minima together, enabling decays within one flux choice.","key_machinery":"The machinery is the four-dimensional $N=1$ supergravity scalar potential for the Kähler moduli, $V=e^K(K^{i\\bar j}D_iW\\bar D_{\\bar j}W-3|W|^2)$, built from a Kähler potential with the classical volume plus the leading $(\\alpha')^3$ correction and a logarithmic volume redefinition, and a superpotential $W=W_0+\\sum_D A_D e^{-a_D T_D}$. The numerical pipeline differentiates this potential automatically, samples starting points inside the Kähler cone by linear programming, solves both the F-term equations $D_iW=0$ and the full extremum equations $\\partial_i V=0$, and validates candidates by checking the Kähler-cone inequalities and positivity of the Hessian. Coexistence emerges from the competition between non-perturbative $e^{-aT}$ terms, which dominate at small volume, and perturbative corrections, which dominate at large volume; the crossing of these two regimes in an intermediate $|W_0|$ window is what puts two minima in one potential.","core_discovery":"The central claim is that for intermediate values of the flux superpotential $W_0$, the same Kähler-moduli scalar potential contains two local minima belonging to different stabilisation scenarios: a small-volume minimum of KKLT or Kähler-uplifted type and a large-volume minimum of LVS type. The paper demonstrates this explicitly on the $h^{1,1}=2$ example $\\mathbb{P}^4[1,1,1,6,9][18]$, where one scan of the $(g_s,W_0)$ plane produced 14,819 coexisting pairs, and reports that LVS-type vacua pair with either KKLT or Kähler-uplifted vacua, never the latter two with each other. Adding $V_{\\rm up}=D_{\\rm up}/\\mathcal{V}^{4/3}$ allows both branches to be lifted independently, giving dS+Minkowski, dS+AdS, and AdS+AdS combinations within one potential, with the small-volume minimum either deeper or shallower than the large-volume one.","pith_inferences":["Inference: if coexisting minima are this common, landscape population dynamics should include decays within one flux sector; such intra-flux decays could change estimates of which vacua dominate and how long metastable dS vacua survive.","Inference: the $|W_0|$ window where the KKLT and LVS branches exchange dominance makes the potential nearly flat between two minima, a natural starting point for volume-modulus inflation models and for kination cosmologies after the saddle disappears.","Inference: the double-minimum window depends on the assumed positive logarithmic correction to the volume; scanning negative values of its coefficient $\\alpha$ would reveal whether coexistence is robust or an artefact of that ansatz.","Inference: the coexisting dS and AdS minima with different volumes provide concrete realisations of the Euclidean AdS-wormhole seed for inflation discussed in the literature, since that mechanism requires exactly a dS vacuum alongside a lower AdS vacuum."],"forward_implications":["Tunnelling rates can now be computed between two minima of the same potential, for example from a small-volume de Sitter vacuum to a large-volume LVS minimum, using concrete potentials where the saddle points are known.","By tuning the anti-D3 uplift coefficient, any combination of AdS, Minkowski, and de Sitter minima can be realised simultaneously in one flux configuration, so dS vacua need not be compared across different flux choices.","As $|W_0|$ is decreased, the LVS minimum shrinks and eventually disappears while the KKLT minimum survives and deepens, confirming that these potentials do not develop a bubble-of-nothing runaway.","Since the coexisting pairs appear for any geometry that supports an LVS-type vacuum, the effect is expected across many of the scanned threefolds with $2\\leq h^{1,1}\\leq 6$."],"supporting_citations":[{"why":"Supplies the KKLT construction that defines the small-volume AdS branch appearing in the coexisting pairs.","marker":"[2]"},{"why":"Supplies the Large Volume Scenario construction that defines the large-volume AdS branch appearing in every coexisting pair.","marker":"[3]"},{"why":"Supplies the Kähler-uplifting mechanism that produces the non-supersymmetric small-volume branch at larger $|W_0|$.","marker":"[10]"},{"why":"Provides the master potential expressions and the hybrid-minima taxonomy that the numerical scans reproduce and extend.","marker":"[13]"},{"why":"Provides the logarithmic F-term solution strategy used to locate KKLT minima numerically.","marker":"[14]"},{"why":"Provides the leading $\\alpha'$ correction to the Kähler potential that balances the non-perturbative terms.","marker":"[17]"},{"why":"Provides the database of Calabi-Yau orientifolds with $h^{1,1}\\leq 6$ used for the large scan.","marker":"[23]"},{"why":"Predicts the $g_s$-$W_0$ trajectory where Kähler-uplifted de Sitter minima should exist, which the numerical scan verifies.","marker":"[60]"},{"why":"Shows coexisting complex-structure flux vacua for fixed fluxes, motivating the analogous Kähler-moduli coexistence found here.","marker":"[25]"}],"fun_headline_variants":["80k Calabi-Yau spaces host coexisting flux vacua","Same flux potential yields KKLT and LVS minima together","String theory: one flux configuration, two distinct vacua","Coexisting KKLT and LVS vacua found in single flux potential","Single flux choice yields both small- and large-volume minima"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Every Kähler modulus must receive a non-perturbative superpotential term, which requires the associated four-cycle to be rigid or rigidifiable; if the large four-cycle in the main worked example is not actually rigid, the coexisting minima shown there would not both appear.","fun_headline_variants_meta":{"raw":{"variants":["80k Calabi-Yau spaces host coexisting flux vacua","Same flux potential yields KKLT and LVS minima together","String theory: one flux configuration, two distinct vacua","Coexisting KKLT and LVS vacua found in single flux potential","Single flux choice yields both small- and large-volume minima"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000684,"raw_usage":{"total_tokens":3160,"prompt_tokens":1061,"completion_tokens":2099,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":677,"completion_tokens_details":{"reasoning_tokens":2013}},"tokens_in":677,"tokens_out":2099,"duration_ms":16454,"temperature":1.0,"reasoning_tokens":2013,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:11:33.351016+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the potential (2.16) for $\\mathbb{P}^4[1,1,1,6,9][18]$ with the same $g_s$, $W_0$, and $\\alpha$ but with the non-perturbative term for the large four-cycle removed; if both minima no longer coexist, the claim rests entirely on that cycle's rigidity. A direct check of whether that divisor has deformation modes that cannot be lifted by allowed worldvolume fluxes would settle the assumption.","supporting_citations":[],"review_version":1}