Scientific Series

I will discuss related aspects of field theories with higher-derivative Lagrangians but second-order equations of motion, with a focus on the Lovelock and Horndeski classes that have found use in modifications to general relativity. In the first half I will investigate when restricting to such terms is and is not well-justified from an effective field theory perspective. In the second half I will discuss how non-perturbative effects, like domain walls and quantum tunneling, are modified in the presence of these kinetic terms

Generally speaking, physicists still experience that computing with paper and pencil is in most cases simpler than computing with a Computer Algebra System.  Although that is true in some cases, the working paradigm is changing: developments in CAS, and particularly recent ones in the Maple system, have resulted in the implementation of most of the mathematical objects and mathematics used in theoretical physics computations, and have dramatically approximated the notation used in the computer to the one used with paper and pencil, diminishing the learning gap and computer-syntax distraction to a strict minimum.  In this talk, the Physics project at Maplesoft will be presented and the resulting Physics package will be illustrated through simple problems in classical field theory, quantum mechanics and general relativity, and through tackling the computations of some recent Physical Review papers in those areas.  In addition to the 10:00 am lecture (taking place in Alice), there will be an afternoon hands-on workshop taking place in the Time Room.

The MAJORANA DEMONSTRATOR (MJD) is a 44-kg array of low-background germanium detectors of which 30kg is made from detectors enriched to 88% in 76Ge. MJD is operating a mile underground in the Sanford Underground Research Laboratory in Lead, SD. Its main purpose is to search for the neutrinoless double-beta decay of 76Ge and to demonstrate the technical feasibility of a tonne-scale Ge-based neutrinoless double-beta decay experiment. It is also capable of direct searches of a variety of dark matter candidates and other physics beyond the Standard Model. In this talk I will review the motivation, design and construction of the MJD, as well as recent results for a the search for bosonic dark matter using commissioning data taken in 2015. I will also discuss the current status of MJD and conclude with a discussion of future plans for MJD and a proposed tonne-scale Ge-based experiment, LEGeND.

There is a growing list of examples where soft factorization theorems in scattering amplitudes can be understood as Ward identities of asymptotic charges. I will review some of these, with emphasis on cases that are not associated to usual conservation laws: leading scalar, subleading photon and sub-subleading graviton soft theorems.

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

I will give an overview of the causal set approach to quantum gravity, and what makes this "fork in the road" distinct from other approaches.  Motivated by deep theorems in Lorentzian geometry, causal set theory (CST) posits that the underlying fabric of spacetime is  atomistic and encoded in a locally finite partially ordered set. In  the continuum  approximation,  the partial order corresponds to the causal structure, and the cardinality to the conformal factor.  Together, these give the approximate continuum geometry.  Lorentz invariance emerges as a consequence, but brings with it a certain  "non-locality”, which distinguishes CST  from other approaches in an essential way. It also makes the  reconstruction of spacetime geometry from the causal set particularly challenging.  I will describe some of the progress we have made in this geometric reconstruction program. I will then describe a particular formulation of CST dynamics inspired by the continuum path integral and discuss what we have learnt so far and where it is taking us. 

The path integral formulation of quantum mechanics has been immensely influential, particularly in high energy physics. However, its applications to quantum circuits has so far been more limited. In this talk I will discuss the sum-over-paths approach to computing transition amplitudes in Clifford circuits. In such a formulation, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action which is provided by the discrete Wigner representation. As an application of the sum-over-paths technique I will show how to recover a version of the Gottesman-Knill theorem, namely that the transition amplitudes in Clifford circuits can be computed efficiently.

I discuss some aspects of boundary conformal field theories (bCFTs). I will demonstrate that free bCFTs have a universal way of satisfying crossing symmetry constraints. I will introduce a simple class of interacting bCFTs where the interaction is restricted to the boundary. Finally, I will discuss relationships between boundary trace anomalies and boundary limits of stress-tensor correlation functions.

Direct detection experiments are rapidly improving their sensitivity to weak scale Dark Matter.  A particular interesting (and minimal) possibility is that the Dark matter interacts with ordinary matter via the exchange of weak bosons: the W, Z, and Higgs.  Dark matter with substantial coupling to the Higgs boson is already under significant tension from limits on spin-independent scattering.  We comment on the power of  spin-dependent scattering as a probe of Z-mediated dark matter, both in a simple effective theory, and in the so-called Singlet-Doublet Model, which we argue is a useful benchmark.  We also review the case where the cosmology of the WIMP is dominated by co-annihilation processes, focusing on the stop co-annihilation region of the Minimal Supersymmetric Standard Model, and discuss prospects for direct detection in this case.

I will describe a tidal effect whereby the decay of primordial gravity waves leaves a permanent shear in the large-scale structure of the Universe. Future large-scale structure surveys - especially radio surveys of high-redshift hydrogen gas - could measure this shear and its spatial dependence to form a map of the initial gravity-wave field. The three dimensional nature of this probe makes it sensitive to the helicity of the gravity waves, allowing for searches for early-Universe gravitational parity violation. Due to the large number of measurable modes in the high-redshift large-scale structure, these tidal imprints could ultimately be more sensitive than searches for CMB B-modes.

It is easy to prove that d-dimensional complex Hilbert space can contain at most d^2 equiangular lines.  But despite considerable evidence and effort, sets of this size have only been proved to exist for finitely many d.  Such sets are relevant in quantum information theory, where they define optimal quantum measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures).  They also correspond to complex projective 2-designs of the minimum possible cardinality.   Numerical evidence points to their existence for all d as orbits of finite Heisenberg groups, the current record being d=844 [Scott-Grassl '17].  However, to date, they are only proven to exist for finitely many d (the current record being d=323 [SG17]) via computer-assisted calculations in number fields of degree increasing with d.  In this talk, I will discuss the structure of these number fields, which turn out to be specific abelian extensions of specific real quadratic number fields [Appleby, Flammia, McConnell, Y. 1604.06098].  Such fields are known to exist by general theorems of class field theory, but until now, had never been found 'explicitly' in Nature.  This contrasts the classical situation for abelian extensions of CM fields, which are generated by the torsion points of abelian varieties with complex multiplication.   All known Heisenberg-covariant SIC-POVMs have unitary symmetries under the associated Weil representation that are intimately related to the structure of the underlying number fields.  A proper understanding of this relationship may ultimately lead to a general proof of their existence in all dimensions, rather than the finite number of examples currently proved to exist. 

We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.