Scientific Series

We argue that theories with multiple axions generically contain a large
number of vacua that can account for the smallness of the cosmological
constant. In a theory with N axions, the dominant instantons with charges Q
determine the discrete symmetry of vacua. Subleading instantons break the
leading periodicity and lift the vacuum degeneracy. For generic integer charges
the number of distinct vacua is given by |det(Q)|~exp(N). Our construction
motivates the existence of a landscape with a vast number of vacua in
four-dimensional effective theories.

Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body systems. Here we employ classical variants of these concepts, in particular Renyi entropies and their associated mutual information, to identify topological order in classical systems.

Like for their quantum counterparts, the presence of topological order can be identified in such classical systems via a universal, subleading contribution to the prevalent volume and boundary laws of the classical Renyi entropies. We demonstrate that an additional subleading O(1) contribution generically arises for all Renyi entropies S(n) with n ≥ 2 when driving the system towards a phase transition, e.g. into a conventionally ordered phase. This additional subleading term, which we dub connectivity contribution, tracks back to partial subsystem ordering and is proportional to the number of connected parts in a given bipartition. Notably, the Levin-Wen summation scheme – typically used to extract the topological contribution to the Renyi entropies – does not fully eliminate this additional connectivity contribution in this classical context. This indicates that the distillation of topological order from Renyi entropies requires an additional level of scrutiny to distinguish topological from non-topological O(1) contributions. This is also the case for quantum systems, for which we discuss which entropies are sensitive to these connectivity contributions. We showcase these findings by extensive numerical simulations of a classical variant of the toric code model, for which we study the stability of topological order in the presence of a magnetic field and at finite temperatures from a Renyi entropy perspective.

We consider 4d N=1 superconformal theories on a cylinder. The partition function on this geometry computes the superconformal index, and can be obtained via the path integral with time direction compactified on a circle and periodic conditions for fermions. We will describe universal formulas for the asymptotics of such partition functions in the limit of very large circle and of very small circle. These limits are completely fixed in terms of coefficients of the Weyl anomaly (a,c). We will explain why supersymmetry is a necessary condition in 4d to establish these higher dimensional analogues of classic results in 2d CFTs. Finally we will discuss some applications and the extension to 6d.

We argue that solutions to the strong CP problem motivate different searches for TeV scale physics at the LHC than are currently being emphasized. We present two solutions to the strong CP problem that require the existence of new colored particles with masses below 10 TeV. New motivated searches at the LHC would provide a strong constraint on these solutions to the strong CP problem.

The next hope to constrain cosmological parameters observationally is in surveys of the large scale structure (LSS) of the universe. LSS has the potential to rival the CMB in cosmological constraints because the number of modes scales like the volume, but the nonlinear clustering due to gravity makes it more difficult to extract primordial parameters. In order to take full advantage of the constraining power of LSS, we must understand it in the quasi-nonlinear regime. The effective field theory (EFT) of LSS provides a consistent way to perturbatively predict the clustering of matter at large distances. In this talk, I will discuss the status of the EFT of LSS and present recent work describing the inclusion of baryons in the EFT approach, including comparisons to N-body simulations.

Solitons in a ferromagnet have interesting dynamics because atomic magnetic moments behave like little gyroscopes. A domain wall in a magnetic wire can be modeled as a bead on a string: it has two soft modes, position and orientation. This "bead" rotates when it is pushed and moves when twisted.

From that one can deduce that the angular momentum is proportional to the domain wall's coordinate and the linear momentum to its azimuthal angle. In fact, the definition of conserved momenta for magnetic solitons has been discussed in the scientific literature for 40 years. A naive attempt to derive them from the application of Noether's theorem yields unphysical, gauge-dependent answers. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons.

I consider the Standard Model as an effective field theory (EFT) at the electroweak scale $v$. At the scale $f\geq v$ I assume a new, strong interaction that breaks the electroweak symmetry dynamically. The Higgs boson arises as a composite pseudo-Nambu-Goldstone boson in these scenarios and is therefore naturally light $(m_{h}\sim v)$. Based on these assumptions and the value of $\xi=v^{2}/f^{2}$, I explain the systematics that governs the effective expansion:\\

For $\xi=\mathcal{O}(1)$ the effective theory is given by a loop expansion, equivalent to an expansion in chiral dimensions (similar to chiral perturbation theory). I will briefly discuss the operators that arise at next-to-leading order ($\mathcal{O}(f^{2} / \Lambda^{2})\simeq \mathcal{O}(1/16\pi^{2})$). On the other hand, in the decoupling limit where $\xi\rightarrow 0$, an expansion in canonical dimension is recovered. The case where $\xi$ is small but non-zero is of phenomenological interest. It leads to a double expansion in $\xi$ and $1/16\pi^{2}$, which captures the expected corrections of a strongly-interacting light Higgs to the Standard Model in a systematic way. \\

Further, I will apply the leading order chiral Lagrangian to current LHC Higgs data. I will show that this gives a QFT justification of the $\kappa$-framework, which is currently used as phenomenological signal-strength parametrization by the experiments at the LHC. I will also present a fit of the leading order chiral Lagrangian to the LHC Higgs data.

In the summer of 2015, the speaker led a team at Microsoft Research, comprised primarily of research interns from seven universities, to demonstrate a social, ambulatory, Mixed Reality system for the first time.  Each intern developed a preliminary, domain-specific exploration of how such a system could be used.  One of the interns, Andrzej Banburski of the Perimeter Institute, demonstrated an interface to Mathematica.  The very concept and terminology of Virtual Reality had been first articulated by the speaker almost four decades earlier precisely in the hopes of experiencing this type of interface.  Mathematical expressions floating in the air is not just more vivid that writing them on a blackboard; a different workflow and mental framework becomes possible.  For instance, functions appear as lenses that can be compounded as they are lined up.  One can peer through a stack of such lenses at different data or starting conditions.  Instead of erasing and replacing portions of expressions on a blackboard, a stack of lenses can fork and merge, so that a range of variations can be explored at once as aspects of a sculptural form.   The purpose is not just to make math more accessible to those who might find this interface more inviting, but to free math from pre-computational, notation-bound conventions.  The speaker will argue that this type of interface, while still only barely explored, could eventually have a significant impact both on computer science and other disciplines, including theoretical physics. 

K-theoretical/Cohomological Hall algebras, associated with the stack of zero-dimensional sheaves on $\mathbb{C}^2$, play a prominent role in the proof, given by Schiffmann and Vasserot, of the AGT conjecture for

(pure) gauge theories on $\mathbb{C}^2$. In the present talk I will describe K-theoretic/Cohomological Hall algebras associated with stacks of torsion sheaves on A-type ALE spaces and their representations; the study of these algebras will provide eventually an approach to prove the AGT conjecture for (pure) gauge theories on A-type ALE spaces. (Work in progress with Olivier Schiffmann.)

This is the first of two talks on recent advances in our understanding of hydrodynamics as a generic theory of near-thermal dynamics of density matrices. In this talk I will focus on the structure of the hydrodynamic gradient expansion subject to the Second Law of thermodynamics. I will present an eightfold classification scheme and an explicit solution at all orders in derivatives of hydrodynamic transport consistent with the Second Law. I will also mention some connections with gravity and argue that the classification hints towards the existence of a gauge theory whose symmetry current is the entropy current. (The topic of my second, independently accessible, talk on Nov 20 will be a detailed field theoretic proposal for how these and other interesting features emerge from microscopic Schwinger-Keldysh formalism.)

Scalable anyonic topological quantum computation requires the error-correction of non-abelian anyon systems. In contrast to abelian topological codes such as the toric code, the design, modelling, and simulation of error-correction protocols for non-abelian anyon codes is still in its infancy. Using a phenomenological noise model, we adapt abelian topological decoding protocols to the non-abelian setting and simulate their behaviour. We also show how to simulate error-correction in universal anyon models by exploiting the special structure of typical noise patterns.

A quantum entanglement is a special kind of correlation; it may yield a strong correlation that is not possible in a classical ensemble, or hide the correlation from all local observables. Especially important is the entanglement that arises from local interactions for its implications in many-body physics and future’s quantum technologies.
I will review a few characteristics of entangled qubits in connection to fault-tolerant quantum information processing, and present a class of long-range entangled many-body states that are ground states of gapped local Hamiltonians on lattices. The class is qualitatively unconventional in many ways, and substantially boosts the richness of many-body entanglement. Implications in mechanisms of localization, renormalization group flow, quantum information storage, and topological order will be discussed.