Which information does a physical description retain?

9 papers · Suggested reading sequence

The manuscripts.

1. 01

   Global Constraints on Higgsing Localized Five-Dimensional Sectors in Compact M-Theory Vacua

   Which local Higgs flows remain available when several singularities share one compact Calabi–Yau threefold?

   Preprint · 2026 · Abstract, PDF & citation ↗

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   Complex deformations of noncompact canonical Calabi–Yau threefold singularities encode Higgs-branch renormalization-group flows of five-dimensional theories. We determine which such flows remain available when several singularities occur in one compact Calabi–Yau threefold. The local sectors are conifold points supporting free hypermultiplets and cones over smooth del Pezzo surfaces of degrees five, six and seven, and over ${\mathbb{P}}^1\times {\mathbb{P}}^1$ of degree eight, engineering the rank-one $E_4,E_3,E_2,E_1$ fixed points. We identify their deformation coordinates with flavor moment maps and derive a compact Abelian gauging matrix from wrapped-M2 charges and divisor pairings. On every choice of local Higgs components, we prove that the invariant deformation-coordinate values attained on the triplet moment-map zero locus in the rigid description are precisely the kernel of this matrix. For connected normal projective threefolds with these exact analytic germs, trivial canonical bundle, $h^1(\mathcal{O})=0$, and a smooth projective crepant resolution of the specified local type, the same kernel is the image of the global first-order deformation space. Combining this identification with the mixed smoothing theorem gives a necessary and sufficient criterion: the kernel must meet the complement of every local discriminant. On the two-dimensional $E_3$ component this requires three separate nonzero coefficients; at $E_4$ it requires five nonzero conic-pencil pairings, identified integrally with the $SU(5)$ diagonal moment-map coordinates. The selected global deformation base is smooth when its relation space projects nontrivially to each selected $E_3$ summand; every tangent on that base integrates to a convergent deformation. Examples distinguish a joint conifold–$E_2$ transition, sectors forced to remain undeformed, and nonzero $E_3$ deformations forced to retain a singularity. These results concern geometric smoothing and invariant moment-map coordinates, not the full finite-Planck hypermultiplet geometry.

2. 02

   Bulk Gauging and Quantum Couplings across a Compact Higgs Transition

   An explicit coupled transition, its integral charge lattice, and its quantum thresholds.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   We study an explicit compact Calabi–Yau transition in which two conifold sectors and a rank-one $E_2$ sector can Higgs only together. The integral relation between their curve classes determines two shared Abelian gaugings and a transition from Hodge numbers $(6,122)$ to $(3,123)$. We compute the primitive surviving charge lattice and its cubic couplings, and show that the flavor gauging cannot remain dynamical in a gravity-decoupling limit with bounded local Kähler scales. On an auxiliary circle the quantum transition contains four conifold states spanning a primitive rank-three electric lattice. Their one-loop thresholds reproduce the integral conifold monodromies. An explicit Laurent mutation and analytic continuation of all eight regular periods identify the genus-zero prepotential of the surviving vectors with that of the smooth phase, including the integral normalization and constant term, and hence its scalar and electromagnetic couplings. At fixed five-dimensional Planck scale the auxiliary-circle limit retains finite bulk gauging, but its closing Kaluza–Klein gap leaves the four conifold states no radius-independent energy range. This limit ends where the del Pezzo surface collapses. On the adjacent face of the nef cone, where only the two nodal curves and two exceptional curves of the del Pezzo surface have zero area, the same four states are massless hypermultiplets of five-dimensional M-theory. The K3 and elliptic fibrations identify a dilaton gauging, an anomaly-consistent six-dimensional $U(2)$ phase and equal compact images of two E-string roots. An exact volume bound excludes the six-dimensional limit on the transition face. A heterotic K3 candidate and topological data are obtained; the global bundle construction and the finite-Planck hypermultiplet geometry remain open.

3. 03

   Magnetic Sheaves and Stability Walls in a Compact Calabi–Yau Transition

   Magnetic sheaves, stability, and numerical contributions on the two sides of a specified compact transition.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   We study magnetic sheaves in a compact Calabi–Yau transition coupling two conifold sectors to a rank-one $E_2$ sector. Fixed-support Hilbert schemes give rank-one numerical Donaldson–Thomas contributions on the rigid ${\mathbb{F}}_1$ and ${\mathbb{P}}^2$ surfaces on the two sides. On a reducible moving divisor, two dual-ideal sheaves are isolated and Gieseker stable, each contributing $+1$; their stability persists along ample polarizations approaching the contraction. Their vanishing first and second self-Ext groups also imply local persistence in smooth polarized deformations of the resolved threefold, but not across its singular transition. An explicit magnetic splitting has one extension mode and a transverse phase alignment near large volume. Using the analytically continued periods of the companion paper, we determine the constituent phase sign at the marked quantum transition and exclude emission of the known light electric particles on a final specified segment. The probe charges nevertheless carry confined magnetic flux after Higgsing. These are component counts and partial wall constraints, not a determination of the physical BPS index at the endpoint. Counts involving complete moving pencils require a separate reduced-member hypothesis, stated in an appendix.

4. 04

   The Higgs Branch of a Compact Calabi–Yau Transition at Finite Planck Mass

   A local normal form for quaternionic Kähler quotients under a freeness hypothesis.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   When a compact Calabi–Yau threefold degenerates, M-theory on it acquires light charged hypermultiplets whose condensation opens a Higgs branch, locally a hyperkähler quotient without gravity. At finite Planck mass the hypermultiplet moduli space is quaternionic Kähler, its metric is unknown, and its moment maps have no additive constant, hence no Fayet–Iliopoulos parameter. We prove a local normal form for quaternionic Kähler quotients near a fixed point at which the moment map vanishes, under a freeness condition on the normal representation: the quotient is locally the product of the fixed set with the flat hyperkähler quotient of that representation, with relative metric corrections of order $r^2$ at distance $r$. Consequently, if exactly $k$ disjoint $(-1,-1)$-curves have zero area on a face of the nef cone with finite gauge couplings, and their classes satisfy one primitive relation ${\sum }_i{a}_i[C_i]=0$ with all $a_i\ne 0$, then, under a regularity hypothesis on the effective supergravity, the Higgs branch opened by the $k$ light hypermultiplets is locally a smooth factor times ${\mathbb{C}}^2/{\mathbb{Z}}_m$, $m={\sum }_i|a_i|$, as without gravity. Transverse to the smooth factor, the order-$r^2$ correction is the curvature of the hypermultiplet manifold restricted to a quaternionic line. A transition with two nodes and a cone over the degree-seven del Pezzo surface has such a face with $k=4$, giving ${\mathbb{C}}^2/{\mathbb{Z}}_4$; where the del Pezzo surface collapses, the Higgs branch defined as the metric completion of the vacua on the smoothed threefold is again of this form. In type IIA string theory, under corresponding hypotheses, the ${\mathbb{C}}^2/{\mathbb{Z}}_k$ point that Greene, Morrison and Vafa expected near $k$ homologous vanishing three-cycles persists at finite Planck mass for these smoothings. A census of toric hypersurfaces finds 5605 faces whose light spectrum has one relation, 372 with $k\ge 3$, all with $m=k$.

5. 05

   The Page Curve Through the Transition: An Order-One Correction to the Diagonal Approximation

   An order-one correction to the diagonal entropy approximation in the west-coast evaporation model.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   In the west-coast model of black hole evaporation, the diagonal approximation computes the entropy of the radiation near the Page time by averaging the entropy of fixed-area states over the black hole’s fluctuating area. We show that this approximation, written level by level, misses an order-one constant: as the area distribution becomes broad, whatever its shape, the exact entropy exceeds it by $-q\log q$, where $q$ is the canonical probability that the black hole is larger than the radiation. The constant arises because the radiation, which has no energy of its own, can resolve area sectors only through the island, and so not those in which the black hole is larger than itself. For a symmetric distribution the excess is half of $\log 2$ at the Page point and largest after it, so the exact transition is asymmetric. The proof reduces the entropy of the exact planar spectrum, a free multiplicative convolution, to a single integral. We compute the first correction and evaluate the constant in Jackiw–Teitelboim gravity. At fixed area, the two-saddle truncation misses the Rényi moments by Catalan factors.

6. 06

   The Page Curve in Higher Dimensions: Phase Transitions, Critical Phenomena, and Finite-Size Broadening

   Critical fluctuations and finite-size Page transitions in a specified canonical random-state model.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   Thermodynamic fluctuations smooth Page transitions, but the usual Gaussian description fails at a black-hole critical point. We determine the resulting finite-size crossover in a canonical random-pure-state model whose density of states is specified by the Reissner–Nordström–AdS entropy. In four or more bulk dimensions, the critical fluctuations obey a quartic limiting law, and the transition width grows as the three-quarter power of the critical black-hole entropy. We derive the leading transition profile and its temperature dependence, and identify the reservoir heat capacity required to preserve the canonical critical behavior. Regular-phase examples provide a comparison with Gaussian fluctuations. The entanglement results hold in the planar limit of the specified random-state model; applications to gravitational entropy transitions require identifying the corresponding state and the fluctuating difference of generalized entropies.

7. 07

   The Page Curve Is Not Enough: Universality, Ensemble Dependence, and Microscopic Ambiguity in Black Hole Information Recovery

   Explicit examples separating entropy curves and spectral averages from finer ensemble and channel information.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   A Page curve constrains radiation entanglement, but its implications for microscopic information recovery depend on which state, ensemble, and channel data are specified. We examine this dependence through explicit finite-dimensional constructions and controlled random-state limits. Two density-matrix ensembles can have the same averaged spectral measure, every averaged replica moment, and the same mean von Neumann entropy, while their entropy and purity fluctuations differ. Fixed Marchenko–Pastur spectra and normalized Wishart spectra give a related large-dimension comparison. At the channel level, an isometry and a replacement channel can reproduce the complete nested radiation trajectory for one input while having different correlations with an external reference. For normalized states, annealed and quenched Rényi entropies have the same von Neumann limit; the derivative of their finite-order difference measures the entropy variance. We derive normalized replica-covariance identities and illustrate their normalization with the standard Haar purity covariance, separating these quantities from entropy of an averaged state. Finally, Gaussian and quartic fluctuations with equal variance give different entropy-transition profiles, illustrating the additional role of joint branch fluctuations and reservoir constraints. These calculations delimit what entropy and spectral agreement establish and specify further comparisons needed in gravitational models.

8. 08

   From Hawking to Marchenko–Pastur: A Guide to the Page Curve and Beyond

   A tutorial from entanglement and Hawking radiation to random matrices, fluctuation laws, and the limits of entropy data.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   This tutorial develops the Page curve program from quantum entanglement and Hawking radiation to holographic entropy, replica wormholes, and random matrix theory. We derive the normalized random-state benchmark and its Marchenko–Pastur limit, explaining the roles of non-crossing partitions and spectral resolvents. We then distinguish averaging conditional entropies from calculating the entropy of a state with fluctuating energy or area. Gaussian broadening, finite reservoirs, and a quartic critical model illustrate how the preparation and the fluctuation law enter this distinction. Exact finite-dimensional examples separate averaged spectra from ensemble fluctuations and radiation data for one input from information about a quantum channel. Normalized annealed and quenched Rényi entropies have a common von Neumann limit, while their finite-order difference and connected replica moments measure additional ensemble information. Throughout, explicit calculations are distinguished from gravitational applications that require further assumptions. The resulting account provides a self-contained introduction to the established methods and to the remaining questions about microscopic information recovery.

9. 09

   Informational Singularities and the Completion of Gravity: Replica Wormholes, Indeterminism, and Cosmic Censorship

   A conceptual distinction between informational completion and geometric completion in quantum gravity.

   Preprint · 2026 · Abstract, PDF & citation ↗

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   Replica wormholes provide the first concrete evidence that quantum gravity can achieve informational completion-restoring a unique, coherent mapping from initial to final quantum states-without achieving geometric completion, the removal or resolution of curvature singularities. I make this distinction precise and use it to extend the framework of generalized indeterminism developed by Azhar and Namjoo into the quantum-gravitational regime. I introduce the concept of an informational singularity: a configuration in which a physical theory fails to provide an existent, unique, and coherent mapping from initial to final quantum states. This concept is logically independent of the geometric singularities of general relativity. The two notions can come apart in both directions: a geometrically smooth region (such as the asymptotic radiation zone in Hawking's calculation) can be informationally singular, while a region with a curvature singularity (such as the interior of an evaporating black hole described by the Page curve) can be informationally complete. I show that the island formula and replica wormhole construction realize informational completion while leaving the geometric singularity untouched, and I confront the ensemble interpretation of the gravitational path integral as a possible obstruction to single-theory completion. Finally, I propose a reformulation of strong cosmic censorship as Informational Cosmic Censorship: the principle that the full quantumgravitational theory provides a coherent state map for generic initial data, regardless of the geometric fate of Cauchy horizons. I argue that this reformulation captures Penrose's original predictability motivation more faithfully than the standard geometric formulation.