On-Shell Covariance of Quantum Field Theory Amplitudes.

Scattering amplitudes in quantum field theory are independent of the field parametrization, which has a natural geometric interpretation as a form of "coordinate invariance." Amplitudes can be expressed in terms of Riemannian curvature tensors, which makes the covariance of amplitudes under nonderivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to all allowed field redefinitions. Amplitudes satisfy a recursion relation to all orders in perturbation theory that closely resembles the application of covariant derivatives to increase the rank of a tensor. This allows us to argue that tree-level amplitudes possess a notion of "on-shell covariance," in that they transform as a tensor under any allowed field redefinition up to a set of terms that vanish when the equations of motion and on-shell momentum constraints are imposed. We highlight a variety of immediate applications to effective field theories.

The muon Smasher's guide.

We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models.

Exponential Hierarchies from Anderson Localization in Theory Space.

We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a one-dimensional disordered wire and the localization of mass eigenstates along a local "theory space" with random mass parameters. Mass eigenstates are localized even at arbitrarily weak disorder, with exponentially suppressed couplings to sites in the theory space. The mechanism is quite general and may be used to exponentially localize fields of any spin. We apply the localization mechanism to two hierarchies in standard model parameters-the smallness of neutrino masses and the ordering of quark masses-and comment on the possible relevance to the electroweak hierarchy problem. This raises the compelling possibility that some of the large hierarchies observed in and beyond the standard model may result from disorder, rather than order.

Quantum field theory of fluids.

The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.