Scientific Series

A simple way to trivially satisfy precision-electroweak and flavor constraints in composite Higgs models is to require a large global symmetry breaking scale, f > 10 TeV. This leads to a tuning of order 10^-4 to obtain the observed Higgs mass, but gives rise to a 'split' spectrum where the strong-sector resonances with masses greater than 10 TeV are separated from the pseudo Nambu-Goldstone bosons, which remain near the electroweak scale. To preserve gauge-coupling unification (due to a composite top quark), the symmetry breaking scale satisfies an upper bound f < 100-1000 TeV, which implies that the resonances are not arbitrarily heavy and may be accessible at future colliders. Furthermore, by identifying dark matter with a pseudo Nambu-Goldstone boson, the smallest coset space containing a stable, scalar singlet and an unbroken SU(5) symmetry is SU(7) / SU(6) x U(1). Interestingly, this coset space also contains a metastable color-triplet pseudo Nambu-Goldstone boson that can decay via a displaced vertex when produced at colliders, leading to a distinctive signal of unnaturalness.

The Atacama Cosmology Telescope (ACT) has been pushing our measurements of the Cosmic Microwave Background on small scales to high resolution and deeper sensitivity since 2008. While ACT stopped taking temperature-only measurements in 2010, ACTPol is now operating with polarisation-sensitive detectors. I will present some of the current ACTPol results in terms of the power spectrum constraints. In addition, I'll highlight some of our recent results using ACTPol data, including detections of both the thermal and the kinetic Sunyaev- Zel'dovich effects through cross-correlation with other probes. I'll discuss the lensing of the small-scale microwave sky as measured by ACT and discus how cross-correlating CMB lensing with other probes gives us a handle on galaxy properties like bias. Finally, I'll discuss the next stage in small-scale CMB cosmology: Advanced ACTPol, which will improve our understanding of the reionisation of the universe - arguably our least constrained epoch to date.

In this talk, I will discuss correlations that can be generated by performing local measurements on bipartite quantum systems. I'll present an algebraic characterization of the set of quantum correlations which allows us to identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a quantum correlation. I will then discuss some examples showing the tightness of our lower bound. Also, the algebraic characterization can be used to express the set of quantum correlations as the projection of an affine section of the cone of completely positive semidefinite matrices. Using this, we identify a semidefinite programming outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín hierarchy, and a linear conic programming problem formulating exactly the quantum value of a nonlocal game. Time permitting, I will discuss other consequences of these conic formulations and some interesting special cases.

This talk is based on work with Antonios Varvitsiotis and Zhaohui Wei, arXiv:1507.00213 and arXiv:1506.07297.

I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and  Balt van Rees. We are attempting to bootstrap massive quantum field theories. 

We formulate a massive S-matrix bootstrap which we analyze both numerically and analytically. We confront our findings with the conformal theory results of lecture 1. We will derive analytic bounds for the couplings in massive 2d QFTs and observe that the Ising field theory with magnetic field lies precisely at the boundary of these bounds.  We conclude with higher dimensional speculations.   

We will discuss a (conjectural) explicit presentation for the equivariant cohomology of Nakajima quiver varieties of type ADE.  This presentation arises as a shadow of the expected symplectic duality between slices to Schubert varieties in the affine Grassmannian and Nakajima quiver varieties (a.k.a. the expected Coulomb and Higgs branches for a quiver gauge theory). 

I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and  Balt van Rees. We are attempting to bootstrap massive quantum field theories. 

A massive quantum field theory can be put in a large AdS space, i.e. in a box. Its correlators define, as they approach the boundary, a conformal theory. The bootstrap of the latter can pose strong constraints on the former as we will describe. We will then initiate a presentation of the general and of the peculiar features of S-matrices in two dimensions.

We studied a holographic superconductor model with a momentum relaxation by employing a linear massless scalar field, which is expected to play a role of impurity via holographic correspondence. By fixing a ratio of impurity/chemical potential, we observed the complex scalar field condensation depending on temperature and computed an electric, thermoelectric, and thermal conductivities. Interestingly, in the presence of the linear massless scalar field, Drude behaviour was shown near a zero frequency regime and the numerical data for the conductivities satisfied Ferrell-Glover-Tinkham (FGT) sum rule. We also numerically checked that the holographic Ward Identity is hold and tried to find if universal law such as Homes law or Uemura’s law is present in our model. However, Homes law was not discovered and Uemera’s law was seen when the charge of the scalar field is 3 and the ratio of the impurity/chemical potential is smaller than about 1/2. 

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like the concept of perfectly independent copies of states used to derive conversion rates. As these idealizations are impossible to implement in practice, such results may be of little consequence for experimentalists.

In this talk I introduce tools to quantify realistic descriptions of resources, applicable for example when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out.

Some resources, like entanglement, can be characterized in terms of copies of local states: we generalize this with operational ways to describe composition and copies of realistic resources, without assuming a tensor product structure.  For others, like thermodynamic work, value is seen as a real function on physical states, like the height of a weight. While value is often expected to behave linearly, that simplification excludes many real-life resources: for example, the operational value of money, in terms of what can be done with it, is hardly linear on the amount of coin, and even has catalytic aspects above certain thresholds. We characterize resources that behave linearly and those that allow for investments - in the extreme, catalytic resources.

This work is an application of the framework introduced in arXiv:1511.08818.

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.

Categorical symplectic geometry studies an invariant of symplectic manifolds called the "Fukaya (A-infinity) category", which consists of the Lagrangian submanifolds and a symplectically-robust intersection theory of these Lagrangians.  Over the last two decades the Fukaya category has emerged as a powerful tool: for instance, it has produced inroads to Arnol'd's Nearby Lagrangians Conjecture, and it allowed Kontsevich to formulate the the Homological Mirror Symmetry conjecture.

In this talk I will describe a project, joint with Satyan Devadoss, Stefan Forcey, and Katrin Wehrheim, which attempts to relate the Fukaya categories of different symplectic manifolds via a notion of functoriality.  After mentioning some analytic results about the singular quilts necessary for this construction, I will describe the combinatorial component: with Devadoss and Forcey we are constructing a family of polytopes that specialize to the associahedra in two different ways, and can be thought of as the 2-categorical version of associahedra.

Generation of accurate mock observations tailored specifically to upcoming surveys such as Advanced ACT, CHIME, and LSST is a key technical challenge in cosmology. Traditional approaches involving N-body simulation are fraught with difficulties due to increasingly large survey volumes and depths. Typically, statistical ensembles can only be realized for a few carefully-chosen parameters, limiting exploration to a significantly restricted cosmological model space. We have developed a new massively parallel algorithm to generate accurate halo masses and positions in a fraction (~1e-3 to 1e-2) of the time taken by N-body simulations. I will present a suite of simulated full sky cluster Sunyaev-Zel’dovich maps that have been produced with this approach, and describe the types of virtual large scale structure observations that are now within reach in the coming years.

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions.  A locality-preserving operation is one which maps local operators to local operators --- for example, a  constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group. 

This is joint work with Oliver Buerschaper, Robert Koenig, Fernando Pastawski and Sumit Sijher.