High Energy Physics

The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when $c=1$, they are related to tau functions of integrable systems of Painlev\'{e} equations. They are also closely related to non-perturbative completions in the topological string theories. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at $c=1$ on $C$ by using the "abelian" Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network and I will show the advantages of this construction. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This is based on a joint work with Andrew Neitzke.

Many fundamental-physics experiments scatter high energy beams off of fixed targets composed of ordinary matter i.e., atoms. When considering the scattering off of atomic electrons we often make the approximation that the electron is free and at rest, however one can ask how good this approximation really is? This becomes especially important in the face of demanding precision goals of certain experiments. For example the planned MuonE experiment will attempt to measure the shape of  $\mu e \rightarrow \mu e$ scattering as a function of angle with a precision of 10 ppm. In this talk I will explain how to systematically include bound-state corrections arising from the difference between a free-and-at-rest electron and those bound in atomic orbitals. When the final state of the atom is not measured, a surprisingly simple and elegant formula can be obtained that reduces the leading order corrections to a single atomic matrix element. New developments related to Coulomb corrections for inelastic systems will also be discussed.  Based on (arXiv:2403.12184, 2407.21752). 

Directional dark matter detectors using diamond as a target material offer a novel solution to overcome solar neutrino backgrounds. Sub-micron damage tracks from nuclear recoils can be read out via advanced quantum sensing techniques with nitrogen-vacancy (NV) centers. I will discuss recent advancements in strain-sensitive quantum interferometry that enable precise strain imaging, paving the way for directional particle detection. These developments highlight the potential of diamond-based detectors for advancing dark matter and neutrino physics, as well as material science applications.

Dark photons and axions are exciting candidates for dark matter, which may be observable through their couplings to electromagnetism or electrons. While many experimental programs have been developed to explore the wide range of parameter space over which these candidates may exist, the mass range corresponding to frequencies below a kHz has been seldom probed by laboratory experiments. In this talk, I will discuss two ongoing efforts to probe this region of parameter space. Both rely on the ability of dark-photon or axion dark matter to source an oscillating magnetic field signal inside an experimental apparatus. In the first case, this magnetic field signal is detected by observing its effect on magnetically levitated (Maglev) systems. The oscillating magnetic field signal sourced by dark matter can drive translational motion of a levitated superconductor or rotational motion of a levitated ferromagnet. As mechanical resonators, Maglev systems are naturally sensitive to lower frequencies, making them well-suited detectors for sub-kHz dark matter candidates. In the second case, we instead consider Earth as the experimental apparatus. That is, we search directly for the oscillating magnetic field signal using unshielded magnetometers located across the Earth's surface. Not only does the signal strength receive an enhancement from the large size of the Earth, but it is also correlated between independent measurements at different locations. I will discuss the search for this signal in existing publicly available magnetometer data maintained by the SuperMAG collaboration, as well as an independent experimental effort, known as SNIPE Hunt, to measure this signal in the field. I will show that both Maglev systems and unshielded magnetometers have the potential to set the leading laboratory constraints on dark-photon and axion dark matter in the sub-kHz regime.

In the framework of Non-Equilibrium Field Theory, I will construct the effective influence functional — generator of non-equilibrium correlation functions — for a mechanical system with degrees of freedom living on a group (e.g. rigid body) interacting with a thermal bath at high temperature. I will derive the constraints on the influence functional following from the group symmetry structure and the DKMS symmetry — generalization of the fluctuation-dissipation theorem. At the linear response level, group symmetry turns out to impose more constraints compared to DKMS. I will illustrate the general formalism with the diffusion in a Fermi gas and exhibit the large-N suppression of the non-linear response. Finally, I will introduce the Universal Bath — the generalization of the Caldeira-Leggett model. It is a dual field theory defined in one extra dimension that reproduces the classical non-equilibrium dynamics of the mechanical system. I will show that in the limit of Ohmic dissipation, when the temperature becomes the only relevant scale at play, the Universal Bath also reproduces the quantum corrections.