Scott Collier, Lorenz Eberhardt, Beatrix Mühlmann

SciPost Phys. 18, 131 (2025) · published 17 April 2025 | Toggle abstract · pdf

We propose a precise duality between pure de Sitter quantum gravity in $2+1$ dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observables, which are identified with the string amplitudes of the complex Liouville string [S. Collier et al., arXiv: 2409.17246]. This establishes a direct connection between integrated cosmological correlators and the resolvents of the matrix integral dual to the complex Liouville string, thereby demonstrating one aspect of the dS$_3$/matrix integral duality. The second aspect concerns the cosmological horizon of the dS static patch and the Gibbons-Hawking entropy it is conjectured to encode. We show that this entropy can be reproduced exactly by counting the entries of the matrix.

Andrew J. Larkoski

SciPost Phys. 18, 130 (2025) · published 17 April 2025 | Toggle abstract · pdf

We study the binary discrimination problem of identification of boosted $H\to gg$ decays from massive QCD jets in a systematic expansion in the strong coupling. Though this decay mode of the Higgs is unlikely to be discovered at the LHC, we analytically demonstrate several features of the likelihood ratio for this problem through explicit analysis of signal and background matrix elements. Through leading-order, we prove that by imposing a constraint on the jet mass and measuring the energy fraction of the softer subjet an improvement of signal to background ratio that is independent of the kinematics of the jets at high boosts can be obtained, and is approximately equal to the inverse of the strong coupling evaluated at the Higgs mass. At next-to-leading order, we construct a powerful discrimination observable through a sort of anomaly detection approach by simply inverting the next-to-leading order $H\to gg$ matrix element with soft gluon emission, which is naturally infrared and collinear safe. Our analytic conclusions are validated in simulated data from all-purpose event generators and subsequent parton showering and demonstrate that the signal-to-background ratio can be improved by a factor of several hundred at high, but accessible, jet energies at the LHC.

Jose Carlos Pelayo, George Bougas, Thomás Fogarty, Thomas Busch, Simeon I. Mistakidis

SciPost Phys. 18, 129 (2025) · published 17 April 2025 | Toggle abstract · pdf

We explore the ground states and dynamics of ultracold atomic droplets in the crossover region from three to two dimensions by solving the two-dimensional and the quasi two-dimensional extended Gross-Pitaevskii equations numerically and with a variational approach. By systematically comparing the droplet properties, we determine the validity regions of the pure two-dimensional description, and therefore the dominance of the logarithmic nonlinear coupling, as a function of the sign of the averaged mean-field interactions and the size of the transverse confinement. One of our main findings is that droplets become substantially extended upon transitioning from negative-to-positive averaged mean-field interactions. This is accompanied by a significant reduction of their binding energies which are approximately inversely proportional to the square of their size. To explore fundamental dynamical properties in the crossover region, we study interaction quenches and show that the droplets perform a periodic breathing motion for modest quench strengths, while larger quench amplitudes lead to continuous expansion exhibiting density ring structures. We also showcase that it is possible to form complex bulk and surface density patterns in anisotropic geometries following the quench. Since we are working with realistic parameters, our results can directly facilitate future experimental realizations.

Sibasish Banerjee, Mauricio Romo, Raphael Senghaas, Johannes Walcher

SciPost Phys. 18, 128 (2025) · published 15 April 2025 | Toggle abstract · pdf

Previous work has given proof and evidence that BPS states in local Calabi-Yau 3-folds can be described and counted by exponential networks on the punctured plane, with the help of a suitable non-abelianization map to the mirror curve. This provides an appealing elementary depiction of moduli of special Lagrangian submanifolds, but so far only a handful of examples have been successfully worked out in detail. In this note, we exhibit an explicit correspondence between torus fixed points of the Hilbert scheme of points on $\mathbb C^2\subset\mathbb C^3$ and anomaly free exponential networks attached to the quadratically framed pair of pants. This description realizes an interesting, and seemingly novel, "age decomposition" of linear partitions. We also provide further details about the networks' perspective on the full D-brane moduli space.

Ivo Souza, Richard M. Martin, Massimiliano Stengel

SciPost Phys. 18, 127 (2025) · published 15 April 2025 | Toggle abstract · pdf

We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $\chi$, and optical gap $E_{\mathrm{G}}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property – the average localization length of valence electrons – from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.