High Energy Physics

Dark matter can be a thermal relic exponentially lighter than
the weak scale without being exponentially weakly coupled. I will present
three mechanisms to obtain light thermal dark matter with sizable
self-interactions and couplings to the Standard Model.

We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric N=4 Yang-Mills theory, three-dimensional conformal field theories and QCD.

An unbroken U(1)' is a minimal possibility for a dark matter self interaction, and may even be associated with dark matter stability. However, such an interaction faces incredibly strong constraints due to collective plasma effects, which dominate over 2-to-2 scattering by an order-of-magnitude of orders-of-magnitude. I will discuss the physics of these collective effects, and show preliminary results of simulation. The constraint of such a self interaction is estimated to be nearly as weak as gravity. 

In previous work it has been observed that the singularity structure of multi-loop scattering amplitudes in planar N=4
super-Yang-Mills theory is evidently dictated by cluster algebras. In my talk I will discuss the interplay between this mathematical
observation and the physical principle that the singularities of Feynman integrals are encoded in the Landau equations.

Effective field theories (EFT) are everywhere in particle physics. Given an EFT, the first question we ask is “what are all the operators consistent with the symmetries and degrees of freedom at a particular expansion order? In this talk I will show how this question can be attacked, and often answered, using an object called a Hilbert series.

I will discuss the recent progress on understanding scattering amplitudes in N=4 SYM beyond the planar limit. I will show that the singularity structure of these amplitudes is very similar to the planar amplitudes suggesting new hidden symmetries to be present in the complete N=4 SYM theory. I will also talk about the extension of this work to N=8 SUGRA by studying the on-shell diagrams in this theory as well as some of the properties of the integrands of loop amplitudes.

Astrophysical observations spanning dwarf galaxies to galaxy clusters indicate that dark matter halos are less dense in their central regions compared to expectations from collisionless dark matter N-body simulations. Using detailed fits to dark matter halos of galaxies and clusters, we show that self-interacting dark matter may provide a consistent solution to the dark matter deficit problem across all scales, even though individual systems exhibit a wide diversity in halo properties. 

The mathematical notion of moonshine relates the theory of finite groups with that of modular objects. The first example, 'Monstrous Moonshine', was clarified in the context of two dimensional conformal field theory in the 90's. In 2010, interest in moonshine in the physics community was reinvigorated when Eguchi et. al. observed representations of the finite group M24 appearing in the elliptic genus of nonlinear sigma models on K3. In 2013, Cheng, Duncan, and Harvey provided a uniform construction of 23 new examples of moonshine, called 'umbral moonshine', of which M24 moonshine is a special case. 

In this talk, I will describe recent work studying the symmetries of certain Landau-Ginzburg orbifold theories that flow in the IR to c=6 N=(4, 4) superconformal field theories on the moduli space of K3 sigma models. We show that discrete symmetries of the UV theory implicate all 23 instances of umbral moonshine, not just M24 moonshine, in symmetries of K3 CFTs. I will then discuss a particular string theory compactification to three dimensions where we find a precise connection to all 23 umbral groups and type IIA string theory on K3.

Over the last few years it has become increasingly clear that there is a deep connection between quantum gravity and quantum information. The connection goes back to the discovery that black holes carry entropy with an amount given by the horizon area. I will present evidence that this is only the tip of the iceberg, and prove that a similar area law applies to more general Renyi entanglement entropies. To demonstrate the simplicity of this prescription, I will use it to calculate the mutual Renyi information between two disks of arbitrary dimension. Furthermore, I will provide quantum corrections to the area law and use it to solve the following important problem: what region of the dual spacetime is described by a subregion in a holographic theory? The answer to this question lies in a new perspective that I will advocate: holography is a quantum error correcting code.

The High-Energy community is only now in the process of fully appreciating the opportunities the LHC provides by producing electroweak-scale resonances beyond threshold. On the one hand this is reflected by changing from the so-called 'kappa framework’ to effective operators and on the other hand by studying Higgs and gauge boson production in processes with large momentum transfer. Accessing more exclusive phase space regions will allow to either discover New Physics or improve Higgs-boson couplings measurements. I will discuss implications of and tools necessary for these measurements, focusing on Higgs boson and Dark Matter phenomenology.

I will discuss a natural basis of CFT operators for probing dual gravitational physics in a diffeomorphism-invariant manner. On the CFT side, these operators are already well-known: they are 'OPE Blocks' that contribute to the Operator Product Expansion with fixed Casimir. On the gravity side, I will show that these OPE blocks are dual to diff-invariant geodesic or surface operators. Our new entry to the holographic dictionary can be understood as an operator generalization of the Ryu-Takayanagi proposal and I will show it gives a unified description for a host of important results in holography.