Scattering amplitudes are the arena where quantum field theory directly meets collider experiments. An excellent model for scattering in QCD is provided by N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors, where the theory becomes integrable, and amplitudes become dual to light-like polygonal Wilson-loop expectation values. The first nontrivial case is the 6-gluon amplitude (hexagonal Wilson loop), which can be computed to 7 loops using a bootstrap which is based on the rigidity of the function space of multiple polylogarithms, together with a few other conditions. It is also possible to bootstrap a particular form factor for the chiral stress-tensor operator to produce 3 gluons, through 8 loops. Remarkably, the two sets of results are related by a mysterious “antipodal” duality, which exchanges the role of branch cuts and derivatives. I will describe how the bootstrapping works and what we know about this new duality.

I’ll review a new, simpler explanation for the large scale geometry of spacetime, presented in our recent preprint arXiv:2201.07279. The basic ingredients are elementary and well-known, namely Einstein’s theory of gravity and Hawking’s method of computing gravitational entropy. The new twist is provided by the boundary conditions we proposed for big bang-type singularities, allowing conformal zeros but imposing CPT symmetry and analyticity at the bang. These boundary conditions allow gravitational instantons for universes with positive Lambda, massless radiation and positive or negative space curvature. Using them, we are able to infer the gravitational entropy for a complete set of quasi-realistic, four-dimensional cosmologies. If the total entropy in radiation exceeds that of Einstein’s static universe, the gravitational entropy exceeds the de Sitter entropy. As the total entropy is increased,  the most probable large-scale geometry for the universe becomes increasingly flat, homogeneous and isotropic. I’ll briefly summarize recent progress towards elaborating this picture into a fully predictive cosmological theory.

Electroweak interactions assign a central role to the gauge group 𝑆𝑈(2)𝐿×𝑈(1)𝑌 , which is either realized linearly (SMEFT) or nonlinearly (e.g., HEFT) in the effective theory obtained when new physics above the electroweak scale is integrated out. Although the discovery of the Higgs boson has made SMEFT the default assumption, nonlinear realization remains possible.

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (∆S = 0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the weak to the O(2 GeV) energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the electroweak scale from QCD operator mixing effects form a closed set, and they result in a 12×12 anomalous dimension matrix. We use the resulting effective Hamiltonian to determine the parity-violating meson-nucleon coupling constants, h^1_π , h^{ 0,1,2}_ ρ , h^{0,1}_ ω , employing the factorization Ansatz and assessments of the pertinent quark charges of the nucleon in lattice QCD at the 2 GeV scale. On this basis, we connect to earlier calculations of low-energy, hadronic parity-violating observables in few-nucleon systems to make theoretical predictions that we compare with recent experimental results, for a global view of the relative importance of the various isosectors. 

Stars have the potential to be excellent dark matter detectors; dark matter could heat them up, destroy them by forming black holes, or modify heat transport. To predict when and how this might happen, we need to compute the scattering rate of dark matter inside stars. In this talk, I will describe how, for a wide range of dark matter models, this requires taking into account collective effects - that is, coherent scattering with many particles inside the star. These effects have been neglected in many previous treatments; I will show how they can enhance or suppress naive predictions for dark matter scattering rates by orders of magnitude. Calculations can be performed systematically by computing in-medium effective propagators, using the apparatus of thermal field theory.

Stars and planets can be ideal playgrounds to discover dark matter. In this talk, I will review a range of dark matter searches using celestial objects, including exoplanets, solar-system planets, and our Sun. I will also discuss a new framework to describe what happens when dark matter is captured inside these objects, and the implications for dark matter search strategies.

Heavy quarks and their bound states are ideal probes of the medium formed in heavy ion collisions.  The resulting hierarchy of scales of in-medium heavy quarkonium makes the combined system ideally suited for treatment using nonrelativistic effective field theories and the formalism of open quantum systems (OQS).  My talk will consist of three parts: in the first, I will present an introduction to nonrelativistic QCD (NRQCD), potential NRQCD (pNRQCD), and the OQS formalism; in the second, I will present the derivation of the master equation governing the evolution of in-medium heavy quarkonium; and in the third, I will discuss solutions of the master equation and present recent phenomenological results for the nuclear modification factor and the elliptic flow compared against experimental measurements.

Classical field theories of scalars that are invariant under a U(1) symmetry can have non-perturbative soliton solutions called Q-balls: spherical bound states that are the energy minimum for a fixed U(1) charge Q. The underlying non-linear differential equations cannot be solved analytically, but I will present analytical approximations that work remarkably well and allow us to understand both ground and excited Q-ball states with ease. The global U(1) symmetry can also be promoted to a gauge symmetry, leading to gauged Q-balls and Q-shells; once again we can find exceptionally good analytic approximations to describe these objects and their stability.