Scientific Series

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.

The talk first offers a brief assessment of the realist and nonrealist understanding of quantum theory, in relation to the role of probability and statistics there from the perspective of quantum information theory, in part in view of several recent developments in quantum information theory in the work of M. G. D’Ariano and L. Hardy, among others. It then argues that what defines quantum theory, both quantum mechanics and quantum field theory, most essentially, including as concerns realism or the lack thereof and the probability and statistics, is a new (vs. classical physics or relativity) role of technology in quantum physics. This role was first considered by Bohr in his analysis of the fundamental role of measuring instruments in the constitution of quantum phenomena, which, he argued, is responsible for the difficulties of providing a realist description of quantum objects and their behavior, and, correlatively, for the irreducibly probabilistic or statistical nature of all quantum predictions. In this paper, I mean “technology” in a broader sense, akin to what the ancient Greeks called “tekhne” (“technique”). It refers the means by which we create new mental and material constructions, such as mathematical, scientific, or philosophical theories or works of art and architecture, or machines, and through which we interact with the world. I shall consider three forms of technology—mathematical, experimental, and digital. The relationships among them were crucial to the discovery of the Higgs boson, and, I argue, are likely to remain equally crucial, indeed unavoidable, in the future of physics, especially quantum physics.

While entanglement entropy of ground states usually follows the area law, violations do exist, and it is important to understand their origin. In 1D they are found to be associated with quantum criticality. Until recently the only established examples of such violation in higher dimensions are free fermion ground states with Fermi surfaces, where it is found that the area law is enhanced by a logarithmic factor.  In Ref. [1], we use multi-dimensional bosonization to provide a simple derivation of this result, and show that the logarithimic factor has a 1D origin. More importantly the bosonization technique allows us to take into account the Fermi liquid interactions, and obtain the leading scaling behavior of the entanglement entropy of Fermi liquids. The central result of our work is that Fermi liquid interactions do not alter the leading scaling behavior of the entanglement entropy, and the logarithmic enhancement of area law is a robust property of the Fermi liquid phase. In sharp contrast to the fermioic systems with Fermi surfaces, quantum critical (or gapless) bosonic systems do not violate the area law above 1D (except for the case discussed below). The fundamental difference lies in the fact that gapless excitations live near a single point (usually origin of momentum space) in such bosonic systems, while they live around an (extended) Fermi surface in Fermi liquids. In Ref. [2], we studied entanglement properties of some specific examples of the so called Bose metal states, in which bosons neither condense (and become a superfluid) nor localize (and

insulate) at T=0. The system supports gapless excitations around ``Bose surfaces", instead of isolated points in momentum space. We showed that similar to free Fermi gas and Fermi liquids, these states violate the entanglement area law in a logarithmic fashion. Compared to ground states, much less is known concretely about entanglement in

(highly) excited states. Going back to free fermion systems, in [3] we show that there exists a duality relation between ground and excited states, and the area law obeyed by ground state turns into a volume law for excited states, something that is widely expected but very hard to prove. Most importantly, we find in appropriate limits the reduced density matrix of a subsystem takes the form of thermal density matrix, providing an explicit example of the eigenstate thermalization hypothesis. Our work [3] explicitly demonstrates how statistical physics emerges from entanglement in a single eigenstate.

[1] Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization, Wenxin Ding, Alexander Seidel, Kun Yang, Phys. Rev. X 2,

011012 (2012).

[2] Violation of Entanglement-Area Law in Bosonic Systems with Bose

Surfaces: Possible Application to Bose Metals, Hsin-Hua Lai, Kun Yang, N.

E. Bonesteel, Phys. Rev. Lett. 111, 210402 (2013).

[3] Entanglement entropy scaling laws and eigenstate thermalization in free fermion systems, Hsin-Hua Lai, Kun Yang, Phys. Rev. B 91,081110 (2015)

The gauged linear sigma model (GLSM) with (0,2) supersymmetry is an excellent tool for generating solutions of the heterotic string. In this talk, I will review a novel mechanism within the (0,2) GLSM for producing target spaces with H-flux, and explore several examples of this type. Along the way, a remarkable relationship between (0,2) gauge anomalies and H-flux will emerge. We will also see hints that many of these spaces require a stringy notion of geometry.

It has been known for a long time that quadratic gravity, which generalizes Einstein gravity with quadratic curvature terms, is renormalizable and asymptotically free in the UV.  However the theory is afflicted with a ghost problem if the perturbative spectrum is taken seriously. We explore the possibility that the dimensional scale of Einstein-Hilbert term is far smaller than the scale where the dimensionless gravitational couplings become strong. The propagation of the gravitational degrees of freedom can change character at this strong interaction scale. Lattice QCD studies show a particular suppression of gluon propagator in the IR, which removes the perturbative gluon from the physical spectrum. We propose that the same fate can apply to the spin-2 ghost. The Planck mass is associated with the strong dynamics scale below which the normal Einstein description can emerge. In this picture both the UV and IR limits have weakly coupled descriptions, similar to perturbative QCD and the chiral Lagrangian. Some implications of a small mass ratio in the theory are considered.

Cosmic neutrinos carry a wealth of information about both cosmology and particle physics, but they are notoriously difficult to observe.  Rapid advancement in measurements of the cosmic microwave background, however, have allowed us to indirectly constrain some properties of the cosmic neutrino background.  I will discuss the current status and future prospects for improving constraints on cosmic neutrinos, focusing in part of the phase shift of acoustic peaks in the cosmic microwave background which results from neutrino fluctuations.  I will also discuss how improved measurements from CMB-Stage IV will naturally constrain a wealth of beyond the standard model physics.

Quantum superpositions of matter are unusually sensitive to decoherence by tiny momentum transfers, in a way that can be made precise with a new diffusion standard quantum limit.  Upcoming matter interferometers will produce unprecedented spatial superpositions of over a million nucleons. What sorts of dark matter scattering events could be seen in these experiments as anomalous decoherence?  We show that it is extremely weak but medium range interaction between matter and dark matter that would be most visible, such as scattering through a Yukawa potential. We construct toy models for these interactions, discuss existing constraints, and delineate the expected sensitivity of forthcoming experiments.  In particular, the OTIMA interferometer developing at the University of Vienna will directly probe many orders of magnitude of parameter space, and the proposed MAQRO satellite experiment would be vastly more sensitive yet.  This is a multidisciplinary talk that will be accessible to a non-specialized audience.