Scientific Series

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.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

 

In my talk I will introduce the spin liquid phases that occur in kagome antiferromagnets, and discuss their physical origin that are closely related with the newly discovered symmetry protected topological phase (SPT). I will first present our numerical (DMRG) study on the kagome XXZ spin model that exhibits two distinct spin liquid phases, namely the chiral spin liquid and the kagome spin liquid (the groundstate of the nearest neighbor kagome Heisenberg model). Both phases extend from the extreme easy-axis limit, through

SU(2) symmetric point, to the pure easy-plane limit. The two phases are separated by a continuous phase transition. Motivated by these numerical results, I will then focus on the easy-axis kagome spin system, and reformulate it as a lattice gauge model. Such formulation enables us to achieve a controlled theoretical description for the spin liquid phases. We then show that the chiral spin liquid is indeed a gauged U(1) SPT phase. On the other hand, we also propose that the kagome spin liquid is a critical spin liquid phase, which can be considered as a gauged deconfined critical point between a SPT and a superfluid phase.

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.

Recent theoretical and experimental efforts have been focused on the identification of excitations in quantum spin ice. Due to their relation to the magnetic monopoles of classical spin ice, their quantum counterparts, called spinons, are a highly sought-after manifestation of fractionalization in frustrated quantum magnets like Yb2Ti2O7. Of particular current interest is the quantum dynamics of spinons, namely, their modes of propagation and interaction with the strongly correlated spin background. To investigate this dynamics, we study excited quantum square ice, as captured by the spin-1/2 checkerboard-lattice XXZ model. We formulate effective free-spinon theories in the strong Ising coupling limit, with spinons either deconfined or artificially confined to nearest-neighbor distance, and calculate the corresponding approximate dynamic spin-structure factors (DSFs). We then evaluate the DSF of the fully interacting model exactly for clusters of up to 72 sites. The resulting spectra allow us to identify dispersive fingerprints of coherent spinon propagation in the correlated ``vacuum'' of quantum square ice within an extended low-energy regime. We thus provide unbiased evidence for the formation of coherent quasiparticles in quantum spin ice above the Ising gap.

Inspired by recent progress into recasting dissipative fluid dynamics within an effective action formalism,

I will show how to embed this problem in holography, where such effective actions can be computed explicitly for the class of relativistic conformal fluids. In particular I will identify the geometric counterpart of certain Goldstone bosons, the light degrees of freedom responsible for the low energy excitations in hydrodynamics. Moreover I will show how the underlying UV Schwinger-Keldysh structure arises at the level of the effective action.

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. 

When a classical system is driven through a continuous phase transition, its nonequilibrium response is universal and exhibits Kibble-Zurek scaling. We explore this dynamical scaling in the context of a three-dimensional topological magnet with fractionalized excitations, namely, the liquid-gas transition of the emergent mobile magnetic monopoles in dipolar spin ice. Using field-mixing and finite-size scaling techniques, we place the critical point of the liquid-gas line in the three-dimensional Ising universality class. We then demonstrate Kibble-Zurek scaling for sweeps of the magnetic field through the critical point. Unusually slow microscopic time scales in spin ice offer a unique opportunity to detect this universal nonequilibrium physics within current experimental capability.

I explain the hierarchy problem of the standard model of particle physics, and discuss some of the ideas which have been put forward to resolve it. I then show that a specific class of theories, built around a framework known as neutral naturalness, can help address this problem while remaining consistent with all current experimental tests. I explain that while certain theories in this class give rise to striking signals, others are extremely difficult to test, and require a detailed study of the properties of the Higgs boson. I consider the implications of these results for the Large Hadron Collider, and for future experimental programs.