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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Gopakumar-Vafa invariants and the Emergent String Conjecture

Abstract The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every infinite-distance limit in the moduli space of a quantum gravity represents either a decompactification limit or an emergent string limit in some duality frame. Within the context of 5d supergravities coming from M-theory compactifications on Calabi-Yau threefolds, we find evidence for this conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which is encoded in the Gopakumar-Vafa invariants of the threefold. In the process, we disuss a testable geometric consequence of the Emergent String Conjecture, and we verify that it is satisfied in all complete intersection Calabi-Yau threefolds in products of projective spaces (CICYs).

Physics↗
DOE OSTI2020

BPS spectra and 3-manifold invariants

We provide a physical definition of new homological invariants H a (M 3 ) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M 3 times a 2-disk, D 2 , whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N = 2 theory T[M 3 ]: D 2 × S 1 half-index, S 2 × S 1 superconformal index, and S 2 × S 1 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M 3 . The last two can be factorized into the product of half-indices. Here, we show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

3-manifold↗
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

BPS chaos

Black holes are chaotic quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of BPS black holes with finite area horizons. On a separate front, the “fuzzball program” has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of \mathcal{N}=4 𝒩 = 4 SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power of N N . In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS as N N is decreased through the recently discovered “fortuity” mechanism. Hence they can plausibly retain their strongly chaotic character.

Chen, Yiming (ORCID:0000000218613230)↗
DOE OSTI2026

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

Extended Supersymmetry↗
DOE OSTI2025

The evaporation of black holes in supergravity

In supergravity, charged rotating black holes are generically driven towards becoming extremal and supersymmetric through the emission of Hawking radiation. Eventually, as the black hole approaches the BPS bound and is close to becoming supersymmetric, quantum gravity corrections become critical to describing the emission of Hawking radiation, making the QFT in curved spacetime approximation inaccurate. In this paper, we compute how such quantum gravity corrections affect the spectrum of Hawking radiation for black holes in $\mathcal{N}$ = 2 supergravity in flatspace. We show that due to such corrections, the spectrum of emitted Hawking radiation for both spin-0 and spin-1/2 particles deviates drastically at low temperatures from the naively expected black-body spectrum. Rather remarkably, the spectrum exhibits a discrete emission line from direct transitions from near-BPS to BPS states, providing the first controlled example where the discreteness of the black hole energies is visible in the emitted Hawking radiation. Similar quantum gravity effects drastically modify the absorption cross-section: BPS black holes are transparent to certain frequencies, while near-BPS black holes appear much larger than the semi-classical prediction.

AdS-CFT Correspondence↗
DOE OSTI2021

The statistical mechanics of near-BPS black holes

Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a 'thermodynamic mass gap' exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity with an AdS2 throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is PSU(1, 1|2). To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a $\mathcal{N}=4$ supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein–Hawking area. Furthermore, our results verify a plethora of string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗