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DOE OSTI2025

On observers in holographic maps

A straightforward gravitational path integral calculation implies that closed universes are trivial, described by a one dimensional Hilbert space. Two recent papers by Harlow-Usatyuk-Zhao and Abdalla-Antonini-Iliesiu-Levine have sought to ameliorate this issue by defining special rules to incorporate observers into the path integral. However, the proposed rules are different, leading to differing results for the Hilbert space dimension. Moreover, the former work offers a holographic map realized using a non-isometric code construction to complement their path integral result and clarify its physics. In this work, we propose a non-isometric code that implements the second construction, allowing thorough comparison. Our prescription may be thought of as simply removing the portion of the map that acts on the observer, while preserving the rest, creating an effective holographic boundary at the observer-environment interface. This proposal can be directly applied to general holographic maps for both open and closed universes of any dimension.

AdS-CFT correspondence↗
DOE OSTI2025

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

AdS-CFT correspondence↗
DOE OSTI2025

The gravitational index of 5d black holes and black strings

The supersymmetric index of 5d black strings and spinning black holes in M-theory is related to that of 4d black holes in type IIA supergravity when both theories are compactified on the same Calabi-Yau threefold. We find the finite-temperature saddles for the 5d gravitational supersymmetric index by uplifting the recently found attractor saddles of the corresponding 4d index. We study uplifts for two types of geometries: 5d black holes and 5d black strings. For 5d black holes, the uplift guarantees that the index of 4d and 5d black holes match. For 5d black strings, the saddle reproduces the microscopic index at leading order in G N , even without the conventional decoupling limit taken in AdS/CFT. In particular, when the temperature is set to be finite in the 5d flat space region, the black string index is computed from an asymptotically flat solution where the AdS throat is absent. Further, as the temperature is lowered and eventually becomes infinitesimally small in the flat space region, the solution admits a novel decoupling limit in which the AdS 3 throat takes the form of a finite-temperature BTZ black hole that is known to compute the index in AdS 3 /CFT 2 . This represents the first step towards understanding holography for supersymmetric observables in flat space, away from the decoupling limit.

AdS-CFT correspondence↗
DOE OSTI2025

Supersymmetry breaking in SYK and the black hole spectrum

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N = 2 Schwarzian theory in which the U(1) R mode becomes massive.

1/N Expansion↗
DOE OSTI2025

Discrete Max-Focusing

The Quantum Focusing Conjecture (QFC) lies at the foundation of holography and semiclassical gravity. The QFC implies the Bousso bound and the Quantum Null Energy Condition (QNEC). The QFC also ensures the consistency of the quantum extremal surface prescription and bulk reconstruction in AdS/CFT. However, the central object in the QFC — the expansion of lightrays — is not defined at points where geodesics enter or leave a null congruence. Moreover, the expansion admits three inequivalent quantum extensions in terms of the conditional max, min, and von Neumann entropies.

AdS-CFT Correspondence↗
DOE OSTI2025

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗
DOE OSTI2025

Higher-derivative corrections in M-theory from precision numerical bootstrap

We study higher-derivative corrections to the graviton scattering amplitude in M-theory, via the stress tensor correlator of 3d$\mathcal{N}$= 8 U(N) k × U(N) –k ABJM theory (dual to graviton scattering in M-theory on AdS 4 × S 7 /ℤ k ). We use the conformal bootstrap combined with an integral constraint derived from supersymmetric localization in order to constrain semishort OPE coefficients appearing in the stress tensor correlator. We obtain islands that are significantly more precise than those in previous studies that did not use the integral constraint. Using these islands, we can estimate the powers and coefficients in a large central charge expansion. This allows us to accurately read off the N 3 LO contribution, from the protected D 6 R 4 correction, and also estimate the N 4 LO contribution, from the unprotected D 8 R 4 correction.

AdS-CFT correspondence↗
DOE OSTI2025

A universal inequality on the unitary 2D CFT partition function

We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}$ + ϵ and below the twist $\frac{c}{12}$ is universal in the large c limit for all β L β R ≠ 4π 2 . The technique of the proof allows us to derive a one-parameter (with parameter α ∈ (0, 1]) family of universal inequalities on the unitary 2D CFT partition function with general central charge c ⩾ 0, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the (β L , β R ) plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality.

AdS-CFT Correspondence↗
DOE OSTI2025

BPS and near-BPS black holes in AdS 5 and their spectrum in $\mathcal{N}$ = 4 SYM

We study quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS 5 × S 5 space, dual to heavy states in 4D N = 4 super Yang-Mills. The analysis provides a gravitational explanation of why 1/16-BPS black holes exhibit an exact degeneracy at large N and why all such states have the same charges, confirming the belief that the superconformal index precisely counts the entropy of extremal black holes. We show the presence of a gap of order N −2 between the 1/16-BPS black holes and the lightest near-BPS black holes within the same charge sector. This is the first example of such a gap for black hole states within the context of AdS 5 holography. We also derive the spectrum of near-BPS states that lie above this gap. Our computation relies on finding the correct version of the N = 2 super-Schwarzian theory which captures the breaking of the SU(1, 1|1) symmetry when the black hole has finite temperature and non-zero chemical potential. Finally, we comment on possible stringy and non-perturbative corrections that can affect the black hole spectrum.

AdS-CFT Correspondence↗
DOE OSTI2025

Holography for BCFTs with multiple boundaries: multi-splitting quenches

We elaborate on the method introduced in arXiv:2403.02165 for holographic duals of Boundary Conformal Field Theories (BCFTs) with multiple boundaries. Naïvely, as the number of boundaries grow large such a calculation becomes unmanageable. We show that is not always the case. Using these advances we calculate the entanglement entropy as a function of time for 1+1-dimensional CFTs that are split into N subsystems. We give explicit results for N = 4 and N = 17. We find that all qualitative differences that arise for larger N are present N = 4.

AdS-CFT correspondence↗
DOE OSTI2025

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity↗
DOE OSTI2025

On tests for baby universes in AdS/CFT

To address a puzzle by Antonini and Rath — where a single CFT state has two bulk duals, one with a baby universe and one without — Engelhardt and Gesteau recently devised a test for baby universes in AdS/CFT. Using the extrapolate dictionary, they showed that the boundary dual of a bulk swap test favored bulk spacetimes without a baby universe, providing evidence against their semiclassical validity. However, recent work suggests that holographic maps should post-select on such closed universes, and we argue that this is consistent with the extrapolate dictionary. We therefore construct a new holographic map for bulk states with baby universes and use this to show that the swap test cannot distinguish between Antonini and Rath’s two candidate bulk duals. This not only allows for a valid semiclassical description of the baby universe, but also enables the application of recent techniques for including observers in holographic maps.

AdS-CFT correspondence↗
DOE OSTI2025

Generalized entropy of gravitational fluctuations

The corrections to holographic entanglement entropy from bulk quantum fields in a classical gravitational background are now well understood. They lead, in particular, to unitary Page curves for evaporating black holes. However, the correct treatment of quantum fluctuations of the metric, including graviton excitations, is a longstanding problem. We provide a gauge-invariant prescription for the generalized entropy of gravitons in anti-de Sitter space in terms of areas and bulk entanglement entropy, generalizing the quantum extremal surface prescription to accommodate fluctuations in the semiclassical spacetime geometry. This task requires a careful treatment of the area operator on the graviton Hilbert space and the definition of a “quantum extremal gauge” in which the extremal surface is unperturbed. It also requires us to determine the correct vacuum modular Hamiltonian for the graviton field, which we fix by requiring that it doesn’t contain a boundary term in extremal gauge. We check our prescription with an explicit computation of the vacuum-subtracted generalized entropy of states containing a graviton in an AdS-Rindler background. Our results exactly match vacuum-subtracted von Neumann entropies for stress-tensor excited states in holographic conformal field theory with d > 2 dimensions. We also use covariant phase space techniques to give a partial proof of our prescription when the entanglement wedge for the background spacetime has a bifurcate Killing horizon. Along the way, we identify a class of perturbative graviton states that have parametrically larger generalized entropy, in the small G N expansion, than any low-energy excitations of an ordinary quantum field.

1/N expansion↗
DOE OSTI2025

2-loop scattering on superstring and supermembrane in flat space

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

AdS-CFT Correspondence↗
DOE OSTI2025

Simple holography in general spacetimes

The simple or “outermost” wedge in AdS is the portion of the entanglement wedge that can be reconstructed with sub-exponential effort from CFT data. Here we furnish a definition in arbitrary spacetimes: given an input wedge a analogous to a CFT boundary region, the simple wedge z(a) is the largest wedge accessible by a “zigzag,” a certain sequence of antinormal lightsheets. We show that z(a) is a throat, and that it is contained in every other throat. This implies that z(a) is unique; that it is contained in the generalized entanglement wedge; and that it reduces to the AdS prescription as a special case. The zigzag explicitly constructs a preferred Cauchy slice that renders the simple wedge accessible from a; thus it adds a novel structure even in AdS. So far, no spacelike construction is known to reproduce these results, even in time-symmetric settings. This may have implications for the modeling of holographic encoding by tensor networks.

AdS-CFT Correspondence↗
DOE OSTI2025

An apologia for islands

Entanglement islands have played a key role in the recent derivation of the Page curve and other progress on the black hole information problem. Arising from the inclusion of connected wormhole saddles in a gravitational replica trick, islands signal that degrees of freedom in the black hole interior are not microscopically independent of the exterior Hawking radiation. Islands were originally discovered in the context of AdS/CFT coupled to an external, nongravitating reservoir, where the coupling gives graviton excitations an anomalous boundary scaling dimension (or “mass”). It has been claimed in the literature that this mass is crucial for the existence of islands and even the Page curve itself. In this paper, however, we explain how entanglement islands can also appear in setups with massless gravitons and no external reservoir, giving a number of examples including the entanglement wedges of boundary CFT regions, of radiation at null infinity in asymptotically flat spacetimes, and of radiation inside a semiclassical but gravitating spacetime. In each case, the Page curve is physically observable and can be determined with sufficiently careful experiments on many copies of the black hole. We give general arguments for the existence of gauge-invariant operators in gravity which are compactly supported to all orders in perturbation theory (whenever no isometries of the background spacetime exist) and refine a recently-proposed explicit construction of such operators. When applied to islands, these results — together with entanglement wedge reconstruction — guarantee that semiclassical operators in the island can be approximated by nonperturbative operators on the Hawking radiation.

AdS-CFT Correspondence↗
DOE OSTI2025

Nonperturbative quantum gravity in a closed Lorentzian universe

We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and real for each α-sector, as induced by spacetime wormholes. This appears to obstruct the conventional quantum-mechanical prescription of assigning probabilities via projection onto a basis of states. While previous approaches have introduced external observers or augmented the theory to resolve this issue, we argue that quantum gravity itself contains all the necessary ingredients to make physical predictions. We demonstrate that the emergence of classical observables and probabilistic outcomes can be understood as a consequence of partial observability: physical observers access only a subsystem of the universe. Tracing out the inaccessible degrees of freedom yields reduced density matrices that encode classical information, with uncertainties exponentially suppressed by the environment’s entropy. We develop this perspective using both the Lorentzian path integral and operator formalisms and support it with a simple microscopic model. Our results show that quantum gravity in a closed universe naturally gives rise to meaningful, robust predictions without recourse to external constructs.

AdS-CFT Correspondence↗
DOE OSTI2025

Open-closed 3d gravity as a random ensemble

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.

AdS-CFT correspondence↗