Scientific Series

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.

The coalescence of black hole-black hole (BHBH), black hole-neutron star (BHNS) and neutron star-neutron star (NSNS) systems are among the most promising sources of gravitational waves (GWs) detectable by Advanced LIGO/Virgo and NANOGrav. In addition, distinct observable electromagnetic radiation may accompany these GWs. Such "multi-messenger" sources can be powerful probes of fundamental physics such as the state of matter under extreme conditions, cosmology, as well as our theories of gravity. However, the identification, detection and interpretation of multimessenger signals from such sources requires careful theoretical modeling through the last stages of the compact binary inspiral, during which all approximations to general relativity break down. The only avenue to theoretically understanding these highly non-linear systems is solving the Einstein equations with the aid of supercomputers. This task is far from trivial: ill-posed formulations of the Einstein equations, gauge issues, the presence of singularities, shocks, and large range of length and time scales inherent to these systems pose strong theoretical and computational challenges. In this talk I will review these challenges, describe state-of-the-art numerical relativity techniques that overcome them, and present results from recent supercomputer simulations of binary NSNSs, and BHBHs around magnetized disks. I will conclude by discussing future directions and applications of numerical relativity.

Light sterile neutrinos are predicted in many theories beyond the Standard Model and may be hinted at in short-baseline data. However cosmological data seems to rule out these neutrinos. Intriguingly, this tension is ameliorated when these new neutrinos are self-interacting. I will explore the impact of this self-interaction on their evolution in the early universe and on the spectrum and flavor of IceCube's ultrahigh energy neutrinos.

Bott periodicity (1956) is a classical and old result in mathematics.
Its easiest incarnation of which concerns Clifford algebras. It says
that, up to Morita equivalence, the real Clifford algebras Cl_1(R),
Cl_2(R), Cl_3(R), etc. repeat with period 8. A similar result holds
for complex Clifford algebras, where the period is now 2. The modern
way of phrasing Bott periodicity in is terms of K-theory: I will
explain how one computes K-theory, and we will see the 8-fold Bott
periodicity emerge from the computations.

Elliptic cohomology is a fancy version of K-theory which can be
thought of as the K-theory of the loop space. A useful slogan is that
K-theory is to quantum mechanics, what elliptic cohomology is to
string theory. This cohomology theory satisfies a version of Bott
periodicity, with period 576. I will explain where that number 576
comes from, and what physical significance this might have.

I conjecture that the above 576-fold periodicity reflects itself in
the classification of 3d TQFTs. Here, the relevant TQFTs are the ones
associated to the chiral Majorana fermion (a type of abelian
Chern-Simons theory of central charge c=1/2). The claim is that the
theory becomes trivial once the central charge reaches 576·1/2 = 288.
The classification of abelian Chern-Simons theories has been
considered by Belov-Moore (2005), who claimed that the periodicity was
reached at c = 24 and later by Kapustin-Saulina (2010), who claimed
that the periodicity was never reached. Our proposal lies strictly in
between those of Belov-Moore and Kapustin-Saulina.

In the de Broglie-Bohm pilot-wave formulation of quantum theory, standard quantum probabilities arise spontaneously through a process of dynamical relaxation that is broadly similar to thermal relaxation in classical physics. If we are to regard this process as the cause of the quantum probabilities we observe today, then we must infer a primordial ‘quantum nonequilibrium’ in the remote past. Such quantum nonequilibrium may have left observable traces today, perhaps in the cosmic microwave background, or in relic particle species that decoupled in the very early universe and that have been sufficiently minimally interacting ever since. The search for the dark matter–that we observe today only through its gravitational interactions–has provided a compendium of particle species that could at least in
principle carry quantum nonequilibrium. If they did indeed exist, nonequilibrium distributions would not only demonstrate the need to reevaluate the canonical quantum formalism, but also generate new phenomena that lie outside the domain of conventional quantum theory, potentially opening up a large domain for investigation. We will develop a simple, parameter free, quantum field theoretical model of spectral measurement, and use it to demonstrate some of the novel effects that could occur to the profiles of the line spectra of such relic particles. We find for instance, line broadening effects that scale with the resolution of the telescope, the possibility of line narrowing and other effects that could cause multiple bumps to form. We use this discussion to comment on possible implications on the indirect search for dark matter.

Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. We present a new family of driven localized Floquet phases, which are analogues of the 1d symmetry protected topological phases familiar from the equilibrium setting. We then propose a classification for such phases.
 

I will explain how to axiomatize the notion of a chiral WZW model using the formalism of VOAs (vertex operator algebras). This class of models is in almost bijective correspondence with pairs (G,k), where G is a connected (not necessarily simply connected) Lie group and k in H^4(BG,Z) is a degree four cohomology class subject to a certain positivity condition. To my surprise, I have found a couple extra models which satisfy all the defining properties of chiral WZW models, but which don't come from pairs (G,k) as above. The simplest such model is the simple current extension of the affine VOA E8xE8 at level (2,2) by the group Z/2. Thus from a quantum perspective, the Lie group E8 x E8 behaves as if it had a non-trivial center.

It is interesting to note that, unlike Chern–Simons theories whose gauge group can be disconnected, the gauge group of a chiral WZW model is necessarily connected. This raises the question of what is the chiral WZW model associated to a disconnected gauge group? Whatever the answer turns out to be, mathematicians will probably need to enlarge the class of objects that they agree to call ‘chiral conformal field theories’ in order to accommodate these yet to be defined models.

I will present some speculations on the matter.

The venerable proton continues to play a central role in fundamental particle physics.   Neutrinos scatter from protons in neutrino oscillation experiments, Weakly Interacting Massive Particles (WIMPs) are expected to scatter from protons in dark matter searches, and electrons or muons are bound by protons in precision atomic spectroscopy.   Our understanding of the proton is an obstacle to the success of next generation experiments hoping to discover CP violation in the lepton sector and determine the neutrino mass hierarchy, discover the particle nature of dark matter, or reveal new interactions such as those that violate lepton universality.  In this talk I present (i) an overview of the current state of knowledge in the neutrino sector, and theoretical advances that will determine a crucial missing ingredient in the predicted signal process of neutrino-nucleus scattering at long baseline neutrino oscillation experiments (ii) the first complete calculation of the scattering cross section of a proton on a static electroweak source, which determines WIMP-nucleus scattering rates at underground direct detection experiments and (iii) the status of the proton radius puzzle, whose most "mundane" resolution requires a 5 standard deviation shift in the value of the Rydberg constant.   I describe how each of these problems has spurred the development of powerful new methods in effective quantum field theory.

We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive proof systems. Specifically, we show that any language in BQP has a quantum interactive proof system with a polynomial-time classical verifier (who can also prepare random single-qubit pure states), and a quantum polynomial-time prover. Here, soundness is unconditional---i.e it holds even for computationally unbounded provers. Compared to prior work achieving similar results, our technique does not require the encoding of the input or of the computation; instead, we rely on encryption of the input (together with a method to perform computations on encrypted inputs), and show that the random choice between three types of input (defining a "computational run", versus two types of "test runs") suffice. As a proof technique, we use a reduction to an entanglement-based protocol; this enables a relatively simple analysis for a situation that has previously remained ambiguous in the literature.