Fall 2016

A stable particle with a weak scale mass and coupling is a well motivated dark matter candidate; one which arises in a variety of models for new physics, including the MSSM. Given the lack of clear evidence for WIMP signatures at direct, indirect and collider searches, we are motivated to look beyond the standard lore. In a model independent framework complementary to LHC monojet searches, we discuss searches at high luminosity colliders for heavy quarkonium decays to dark matter particles with masses below the weak scale. Also, we investigate unconventional MSSM parameter space by relaxing commonly made simplifying assumptions, such as minimal flavor violation, then reexamining constraints from direct dark matter detection and the associated nuclear physics uncertainties.  Finally, moving from a single particle to a multi-component dark matter framework, we consider the impact of many particles decaying in the early universe on the application of constraints from light element abundances and the CMB.

The axion was predicted a long time ago in a symmetry-based solution to the QCD strong CP problem. As a cold dark matter candidate, the axion particle can potentially form a Bose-Einstein condensate state as an axion star. In this talk, I will discuss a new way to detect axion stars via its surrounding dust or planets.

The past summer has seen an intense flurry of activity around the topic low-energy dualities that has uncovered a veritable web of 3-dimensional dualities relating a number of non-supersymmetric bosonic and fermionic theories. Moreover, these dualities find a very satisfying and direct “real-world” application to the physics of topological quantum matter. In this talk, I will give a more-or-less pedagogical introduction to the subject of low energy dualities and review some of the more recent developments in the field. 

Motivated by black hole physics, we study the relationship between quantum chaos, holographic complexity, and pseudo randomness. First, we develop a diagnostic of quantum chaos by directly considering the time evolution of a simple local operator. This leads us to out-of-time-order correlation functions as a natural measure of quantum chaos. We explain how such correlators are natural probes of the black hole interior in holography. Using tools from quantum information, we use a generalization of these correlators to develop a lower bound on the computational complexity of an ensemble of unitary operators. Finally, we introduce a conjecture that the quantum complexity of a holographic state is dual to the spacetime action of the black hole interior.

We present a new mechanism to stabilize the electroweak hierarchy. We introduce N copies of the Standard Model with varying values of the Higgs mass parameter. This generically yields a sector whose weak scale is parametrically removed from the cutoff by a factor of 1/√{N}. Ensuring that reheating deposits a majority of the total energy density into this lightest sector requires a modification of the standard cosmological history, providing a powerful probe of the mechanism. Current and near-future experiments will explore much of the natural parameter space. Furthermore, supersymmetric completions which preserve grand unification predict superpartners with mass below mW × Mpl / MGUT 〜 10 TeV.

We recast 4D scattering amplitudes and their soft limits as correlators of a 2D CFT on the celestial sphere.  Our construction relies on a foliation of 4D flat space into a family of 3D hyperbolic geometries to which the AdS3/CFT2 dictionary is directly applicable.  By reformulating 4D scattering amplitudes as 3D Witten diagrams dual to 2D correlators, we show how the Ward identities of the 2D CFT are equivalent to the 4D soft theorems.  Moreover, we demonstrate how the infinite-dimensional Kac-Moody and Virasoro algebras of the 2D CFT are manifested as the asymptotic symmetries of 4D flat space.  Finally, we discuss the interpretation of 4D electromagnetic and gravitational memory effects as a certain version of the 3D Aharonov-Bohm effect.

In the study of purely quantum phenomena, such as occur in double slit experiments, etc., it is useful to introduce modular variables rather than the more familiar positions and momenta. I will first review these variables and then show how they may be understood on a mathematical level as a generalization of geometric quantization. Playing a central role here is the Heisenberg group and its commutative subgroups. Our usual notion of classical space can be identified with a particular choice of commutative subgroup corresponding to a classical Lagrangian subspace of phase space, that is a choice of classical polarization. There are however purely quantum polarizations that correspond to a choice of modular variables. Such quantizations generically involve a dimensional scale in addition to \hbar. In simple quantum systems, the scale is set contextually, for example by a slit spacing.  A new notion of quantum space(time) emerges if we suppose instead that the scale is fundamental. I will provide substantial evidence that, contrary to the textbook accounts, this mechanism is present in ordinary string theory. Thus string theory describes an inherently quantum gravitational theory, for which the usual string constructions correspond to certain semi-classical limits with a local space-time interpretation, with string dualities manifest. 

Causality imposes constraints on the coupling constants in perturbative effective field theory, which have played a role in understanding scattering amplitudes, the a-theorem for renormalization group flows, and higher curvature corrections in quantum gravity. I will describe similar constraints on strongly interacting theories. In one limit, these constraints imply the averaged null energy condition, which links causality to the inequalities obeyed by quantum information. Then, in large-N conformal field theory, I'll describe how causality tightly constrains the stress tensor correlation functions, and points directly toward the emergence of Einstein gravity in the holographic dual.

We will review the two paradigmatic examples of AdS/CFT: maximally supersymmetric N=4 super Yang-Mills in 4d and N=6 supersymmetric Chern-Simons in 3d. We will discuss supersymmetric Wilson loops (WL) in these theories and their exact computation in gauge theory via Localization techniques. We will turn to the string side and show how to reproduce the WL strong coupling expansion from semiclassical string worldsheets.

The past summer has seen an intense flurry of activity around the topic low-energy dualities that has uncovered a veritable web of 3-dimensional dualities relating a number of non-supersymmetric bosonic and fermionic theories. Moreover, these dualities find a very satisfying and direct “real-world” application to the physics of topological quantum matter. In this talk, I will give a more-or-less pedagogical introduction to the subject of low energy dualities and review some of the more recent developments in the field. 

While the current vacuum energy of the Universe is very small, in our standard cosmological picture it has been much larger at earlier epochs. We try to address the question of what are possible ways to try to experimentally verify this. One direction is to look for systems where vacuum energy constitutes a non-negligible fraction of the total energy, and study the properties of those. Another possibility is to focus on the epochs around cosmic phase transitions, when the vacuum energy is of the same order as the total energy. Along these lines we investigate properties of neutron stars and the imprint of phase transitions on primordial gravitational waves.

I will give an overview of some recent developments in moonshine including umbral moonshine and its connection to K3 surfaces and Niemeier lattices. I will then discuss a new form of moonshine related to skew-holomorphic Jacobi forms and discuss briefly some of the relations between these new moonshines and the original moonshine associated to the Monster sporadic group.