Scientific Series

I will summarize recent progress in uncovering the analytic structure of scattering amplitudes. The overarching theme will be exploiting new intricate ways of analytically continuing time, extending beyond the Wick rotation. I will highlight a broad range of applications: from high-precision calculations in particle physics, through computations of gravitational waves, to formal topics in the scattering of strings.

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I will talk about the boundary vertex operator algebra of topologically twisted 3d N=4 rank-zero SCFTs. The latter is recently introduced family of N=4 SCFTs with zero-dimensional Higgs and Coulomb branches, which are expected to support rational VOAs at the boundary. I will discuss the construction of the simplest class of rank-zero SCFTs T_r, and argue that they admit the simple affine VOAs L_r(osp(1|2)) at their boundary. In the simplest case, this leads to a physical realization of a novel level-rank duality between L_1(osp(1|2)) and the Virasoro minimal model M(2,5).

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While the standard $\Lambda$CDM model provides an astonishing fit to cosmological data, there is a 4-6 $\sigma$ tension in the Hubble constant, $H_0$, between the value inferred from early-Universe observables, Planck CMB anisotropy spectra, and the value determined by local measurements from SH0ES collaboration using Type 1a supernovae calibrated with Cepheid variables. As an effort to solve this tension, we develop a method of searching for data-driven solutions to the Hubble tension given cosmological dataset, based on the standard Fisher bias formalism. Taking as proof of principle the case of a time-varying electron mass, and focusing first on Planck CMB data, we demonstrate a modified recombination can solve the Hubble tension and lower $S_8$ to better match weak lensing measurements. Once baryonic acoustic oscillation and uncalibrated supernovae data are included, it is not possible to fully solve the tension with perturbative modifications to recombination. The method we develop in this work can be a useful tool to search for many other possible extensions to the $\Lambda$CDM model, and is expected to inspire a model-building effort from the cosmology and particle physics community.

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In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise
channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates — meaning it is never too "flat" — regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both
of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results. This talk is based on arXiv:2306.16659.

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The existence of fermionic compact objects, such as neutron stars, is supported by a plethora of observational evidence — an intriguing idea is whether one can construct stars made up of the bosonic counterparts. Such theoretical objects are called boson stars, proposed to make up a fraction of the dark matter in our Universe and claimed to be promising horizonless black hole mimickers. In this talk I will discuss the state-of-the-art of numerical evolutions of boson star models in spherical symmetry. In particular, I will discuss how improper initial data construction can lead to spurious physical effects in the evolution of boson star mergers and introduce methods, necessary to remedy such spurious features. I will present our results on boson star head-on collisions of various mass ratios, highlighting the differences from the black hole mergers. Lastly, I will discuss our recent results on the high-precision numerical relativity simulations of quasi-circular boson star inspirals in pursuit of understanding the implications of boson star signatures on the LIGO-Virgo-KAGRA observations.

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In this talk I will show how the gravitational potentials generated by ultralight dark matter halos interact with gravitational waves, resonantly amplifying them. Significant amplifications can be achieved in dense dark matter environments, where the Floquet exponent is increased. The frequency of the amplified gravitational wave is equal to the axion mass when one requires resonance in the first band. For some masses considered, the gravitational wave frequencies fall within the Pulsar Timing Array range, representing an interesting possibility to test ultralight axions as dark matter candidates.

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The sexaquark, a hypothetical stable and neutral six-quark state, has been recently proposed as a dark matter candidate. Here, I argue it is very unlikely sexaquarks could consistently compose more than a billionth of the dark matter abundance for a wide range of scattering cross sections and annihilation rates. To draw these conclusions, I will connect several topics, including the sexaquark freeze-out abundance, dark matter direct detection constraints, neutrino experiments, and accumulation mechanisms for sexaquarks in the Earth. I will show how the sexaquark cosmology enforces that a large contribution to dark matter is only possible with a similarly large antisexaquark population. This population, however, would leave a stark annihilation signal in a detector such as Super-Kamiokande. I will summarize with how sexaquarks as a large component of the dark matter is incompatible with current observational data.

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The fundamental nature of dark matter and dark energy remains unknown and requires new physics to explain. This talk will present a cosmological quest to understand the properties of these two dominant but invisible components of our universe. I will present my work on early and late-universe searches for the identity of dark matter, and discuss cosmological limits on its mass, interactions with Standard Model, and production mechanisms, using the measurements of Big Bang Nucleosynthesis, Cosmic Microwave Background, 21-cm, and cosmic structure. Within the next decade, upcoming surveys will dramatically improve our measurements of these probes, enabling new insights into the invisible universe. If time permits, I will briefly introduce my work on cosmological searches for dark energy, as well as modified gravity.

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Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before reaching the horizon. There does not seem to be a good understanding of how to properly model a reflecting surface in numerical relativity, as the vast majority of the literature avoids the implementation of artificial boundaries, or applies transmitting boundary conditions. Here, we present a framework for reflecting a scalar field in a fully dynamical spherically symmetric spacetime, and implement it numerically. We study the evolution of a wave packet in this situation and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole. This opens the door to model exotic near-horizon physics within full numerical relativity.

I introduce a unified framework for interpreting neural network classifiers tailored toward automated scientific discovery. In contrast to neural network-based regression, for classification, it is in general impossible to find a one-to-one mapping from the neural network to a symbolic equation even if the neural network itself bases its classification on a quantity that can be written as a closed-form equation. In this paper, I embed a trained neural network into an equivalence class of classifying functions that base their decisions on the same quantity. I interpret neural networks by finding an intersection between this equivalence class and human-readable equations defined by the search space of symbolic regression. The approach is not limited to classifiers or full neural networks and can be applied to arbitrary neurons in hidden layers or latent spaces or to simplify the process of interpreting neural network regressors.

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I’ll give a review of extended phase space in gauge theories and/or diffeomorphism-invariant theories, beginning with its original conception up to our most recent work. The primary focus in a classical theory is on the proper representation of symmetries and gauge symmetries on phase space. Correspondingly, this is understood in the quantum theory through the crossed product construction and conditional expectation. I’ll discuss several examples.

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