Scientific Series

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions. This is joint work with Ersen Bilgin.

The AdS/CFT correspondence relates large-N, planar quantum gauge theories to string theory on the Anti-de-Sitter background. I will discuss exact results in field theories with AdS duals, which can be obtained with the help of diagram resummations, mapping to quantum spin chains and two-dimensional sigma-models.

I revisit an example of stronger-than-quantum correlations that was discovered by Ernst Specker in 1960. The example was introduced as a parable wherein an over-protective seer sets a simple prediction task to his daughter's suitors. The challenge cannot be met because the seer asks the suitors for a noncontextual assignment of values but measures a system for which the statistics are inconsistent with such an assignment. I will show how by generalizing these sorts of correlations, one is led naturally to some well-known proofs of nonlocality and contextuality, and to some new ones. Specker's parable involves a kind of complementarity that does not arise in quantum theory - three measurements that can be implemented jointly pairwise but not triplewise -- and therefore prompts the question of what sorts of foundational principles might rule out this kind of complementarity. This is joint work with Howard Wiseman and Yeong-Cherng Liang.

The entropy outside of an event horizon can never decrease if one includes a term proportional to the horizon area. For a long time, this astonishing result had only been shown for quantum fields that are in an approximately steady state. I will describe a new proof of the generalized second law for arbitrary slices of semiclassical, rapidly-changing horizons. I will start with the simplest case, Rindler horizons, and then describe how the proof can be adapted to other cases (black holes, de Sitter, etc.) by restricting the field algebra to the horizon. The generalized second law holds because the horizon is invariant under a larger symmetry group than the rest of the spacetime.

A remarkable result from heavy ion collisions at the Relativistic Heavy Ion Collider is that shortly after a collision, the medium produced behaves as a nearly ideal liquid. The system is very dynamic and evolves from a state of two colliding nuclei to a liquid in a time roughly equivalent to the time it takes light to cross a proton. Understanding the mechanisms behind the rapid approach to a liquid state is a challenging task. In recent years holography has emerged as a powerful tool to study non-equilibrium phenomena, mapping the (challenging) dynamics of quantum systems onto the dynamics of classical gravitational systems. The creation of a liquid in a quantum theory maps onto the classical process of gravitational collapse and black hole formation. I will describe how one can use holography to study processes which mimic the dynamics of heavy ion collisions.

Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting models expanded about a suitable pseudofree theory [differing from a free theory by an $O(\hbar^2)$ term]. This procedure not only provides acceptable solutions for models for which no acceptable solution currently exists, e.g., $\varphi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\varphi^4_n$, for $n=2,3$.

"Conventional" superconductivity is one of the most dramatic phenomena in condensed matter physics, and yet by the 1970's it was fully understood - a solved problem much like quantum electrodynamics. The discovery of high temperature superconductivity changed all that and opened the door, not only to higher Tc's, but also to a wealth of even more exotic phenomena, including things like topologically ordered superconductors with factional vortices and non-Abelian statistics. I will describe some of the evolution of the field of exotic superconductivity, with a focus on recent theoretical and experimental work which sheds light on whether strontium ruthenate supports topological chiral superconductivity.

In this talk we quickly review the basics of the modal "toy model" of quantum theory described by Schumacher in his September 22 colloquium at PI. We then consider how the theory addresses more general open systems. Because the modal theory has a more primitive mathematical structure than actual quantum mechanics, it lacks density operators, positive operator measurements, and completely positive maps. As we will show, however, modal quantum theory has an elegant description of the states, effects and operations of open modal systems -- a description with close analogies to actual quantum mechanics.

If dark matter consists of a multiplet with small mass splittings, it is possible to simultaneously account for DAMA/CoGeNT hints of direct detection and the INTEGRAL 511 keV gamma ray excess from the galactic center; such dark matter must be in the 4-12 GeV mass range. I present scenarios where the DM transforms under a hidden SU(2) that can account for these observations. These models can be tested in low-energy beam dump experiments, like APEX. To explain PAMELA/Fermi excess electrons from dark matter annihilations, heavier TeV scale DM is required. I will present new more stringent constraints from Fermi gamma ray data that tend to rule out such models. However we find a loophole: DM annihilations in a nearby DM subhalo, between us and the galactic center, could provide the excess leptons while respecting gamma ray constraints.

This talk will focus on hypermultiplet moduli spaces of various N=2 supersymmetric gauge theories in (3+1)d. In the first part of the talk, we discuss the moduli space of instantons on C^2. For the classical groups, the ADHM construction of the moduli space can be realised on the Higgs branch of N=2 gauge theories on D3-branes probing D7-branes. No known construction is available for exceptional groups. We go over the computation of Hilbert series for the one instanton moduli space and show that it is possible to count all chiral operators on the moduli space even though a Lagrangian is not known for exceptional gauge groups. In the second part, we discuss a class of N=2 gauge theories on two M5-branes wrapping Riemann surfaces. This talk will go over Hilbert series for the hypermultiplet moduli space of such theories and show that it is possible to count all chiral operators on the hypermultiplet moduli space for any genus and any number of punctures of the Riemann surface.

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the very inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on an analysis of what it may mean for one tensor to depend in the proper way on another, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime.

Over the last decade there has been strong interest in the theory and phenomenology of particle propagation in quantum spacetime. The main results concern possible Planck-scale modifications of the "dispersion" relation between energy and momentum of a particle. I review results establishing that these modifications can be tested using observations of gamma rays from sources at cosmological distances. And I report recent progress in the understanding of the implications of spacetime expansion for such studies. I also discuss recent preliminary results suggesting that the same Planck-scale modifications of the dispersion relation might have an unexpected role in gravitational collapse.