Scientific Series

Scattering amplitudes in gauge theories and gravity have extraordinary properties that are completely invisible in the textbook formulation of quantum field theory using Feynman diagrams. In the standard approach--going back to the birth of quantum field theory--space-time locality and quantum-mechanical unitarity are made manifest at the cost of introducing huge gauge redundancies in our description of physics. As a consequence, apart from the very simplest processes, Feynman diagram calculations are enormously complicated, while the final results turn out to be amazingly simple, exhibiting hidden infinite-dimensional symmetries. This strongly suggests the existence of a new formulation of quantum field theory where locality and unitarity are derived concepts, while other physical principles are made more manifest. Rapid advances have been made towards uncovering this new picture, especially for the maximally supersymmetric gauge theory in four dimensions. These developments have interwoven and exposed connections between a remarkable collection of ideas from string theory, twistor theory and integrable systems, as well as a number of new mathematical structures in algebraic geometry. In this talk I will review the current state of this subject and and describe a number of ongoing directions of research.

I will discuss a novel approach to time-dependent background fields of string theory, which allows the identification of configurations which satisfy the conformal invariance conditions to all orders in the Regge slope parameter alpha'. I will present a graviton, dilaton and tachyon configuration which is a resummation of all orders in the Regge slope and is shown to satisfy the conformal invariance conditions order by order, to all orders in alpha', up to field redefinitions which do not change the dependence of the fields on the target space-time coordinates, due to a property termed as "homogeneity" of the Weyl anomaly coefficients. It describes an inflationary universe in the sigma-model frame, while in the Einstein frame it corresponds either to a de Sitter or to a power-law universe, depending on the values of the dilaton and the tachyon amplitudes. Possible ways to connect these different solutions, which may correspond to different epochs of the universe, will also be discussed.

Gauge/gravity duality, a concept which emerged from string theory, holds promise for revealing the secrets of certain strongly interacting real world condensed matter systems. Historically, string theorists presented their subject as a promising framework for a quantum theory of gravity. More recently, the AdS/CFT correspondence and gauge/gravity dualities have emerged as powerful tools for using what we already know about gravity to investigate the properties of strongly interacting field theories. I will cherry pick and discuss a few recent developments where black holes are used to calculate the thermodynamic and transport properties of quantum critical systems, superconductors, and superfluids.

Symmetric monoidal categories provide a convenient and enlightening framework within which to compare and contrast physical theories on a common mathematical footing. In this talk we consider two theories: stabiliser qubit quantum mechanics and the toy bit theory proposed by Rob Spekkens. Expressed in the categorical framework the two theories look very similar mathematically, reflecting their common physical features. There are differences though: in particular a finite Abelian group emerges naturally in the categorical framework, and this group is different in each case ($Z_4$ for the stabiliser theory and $Z_2 \times Z_2$ for the toy bit theory). It turns out that this mathematical difference corresponds directly with a key physical difference between the theories: the stabiliser theory cannot be modelled by local hidden variables, while the toy bit theory can. This analysis can be extended to other Abelian groups yielding a group-theoretic criterion for determining the possibility of local hidden variable interpretations for other physical theories.

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Some of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. In this talk, I will outline progress on the theoretical description of eternal inflation and bubble collisions, and present results from the first search for the effects of bubble collisions in the WMAP 7-year data.

N=8 supergravity in 4 dimensions exhibits a surprisingly favorable UV behavior -- it is known from explicit computations that the 4-point amplitudes in N=8 supergravity are finite up to 4-loop order. I explain how a "matrix-element approach" can be used to study candidate counterterms for UV divergences in this theory. This approach both demystifies the finiteness found in previous computations, and predicts finiteness of arbitrary n-point amplitudes in N=8 supergravity below the 7-loop order. It also points to the 7-loop 4-point amplitude as the first amplitude whose finiteness is not guaranteed by any known symmetry of the theory.

Quantum mechanics does not allow us to measure all possible combinations of observables on one system. Even in the simplest case of two observables we know, that measuring one of the observables changes the system in such way, that the other measurement will not give us desired precise information about the state of the system. Prominent examples of such observables are measurement of position and momentum of a particle, or measuring spin along two orthogonal directions. However, once we accept the possibility of imprecise measurements, we can consider to perform such measurement within one experiment. This is the basis of the notion of coexistence. I will present the basics of coexistence by showing how to perform the spin measurement in two directions, while considering the imprecision of the measurement described by POVMs. We can also go a little further and consider coexistence of instruments, i.e. measurements, where on the output besides classical information we are also left out with quantum post-measurement state.

Recent observations first made in string theory led to the realization that introducing various ``deformations" (finite volume, appropriate double-trace operators...) allows for an analytic study of many nonperturbative aspects of arbitrary four-dimensional gauge theories. Notably, the confinement mechanism, the generation of mass gap, and, in some cases, chiral symmetry breaking can be studied in a theoretically controlled manner. In this talk, I will review: i.) the ideas and tools involved, ii.) the main results obtained so far in this approach (and its limitations), iii.) our understanding of its relation to other approaches to (non-)supersymmetric gauge dynamics, iv.) ongoing and possible future work.

To a first approximation, everything that happens at the Large Hadron Collider at CERN is a strong interaction process. If signals of supersymmetric particles or other new states are found at the LHC, the events that produce those signals will represent parts per trillion of the total sample of proton-proton scattering events and parts per billion of the sample of events with hard scattering of quarks and gluons. Can we predict the rates of QCD processes well enough to control their contribution to a tantalizing signal? What physics insights can assist this process? Can string theory help? In this lecture, I will describe the current status of Quantum Chromodynamics and its application to the predictions for hadron colliders. Note: Those who would like more background on the LHC should attend my talk at the Physics Department Colloquium of the University of Waterloo, Thursday, Jan. 13, at 4:00 pm: The Search for New Elementary Particles at the CERN Large Hadron Collider

Mathematics and physics can come together to the benefit of both fields, particularly in the case of Calabi-Yau spaces and string theory---our leading attempt to explain the universe to date. The audience will gain a sense of how mathematicians think and approach the world and realize that mathematics does not have to be a wholly abstract discipline, disconnected from everyday phenomena, but it is instead crucial to our understanding of the physical world.

Strong lensing galaxy clusters provide promising probes of cosmological structure formation. Strong lensing halos can be identified in cosmological simulations through ray tracing techniques and their properties measured. Previous studies have found some evidence that strong lensing clusters are more concentrated than expected, with possible explanations including baryonic effects or more exotic physics such as early dark energy. Using Sunyaev-Zeldovich (SZ) observations to measure the mass on large scales and strong lensing mass modeling for small scales, we find that the clusters are more concentrated than expected at the 97% confidence level. We also investigate the placement of lensed images with respect to the SZ gas and Brightest Cluster Galaxy orientations. I will also discuss the redshift evolution of radio Active Galactic Nuclei in clusters, which is relevant for determining cosmological parameters from SZ surveys as well as for understanding the energy budgets in cluster cores.

Hints for the possibility of two times emerged in M-theory in 1995. If taken seriously this required new concepts that could solve unitarity (ghost) and causality problems so that physics could be described sensibly in a spacetime with two times. The necessary concept turned out to be a gauge symmetry in phase space. This is an unfamiliar concept, but is one that extends Einstein's approach to the formulation of fundamental equations of physics, by removing the perspective of the observer, not only in position space but more generally in phase space. This approach led in 1998 to what is now called 2T-physics, which has been formulated so far in classical and quantum mechanics, field theory and partially in string theory. In this lecture I will explain the fundamental aspects of 2T-physics, and will outline the progress from classical mechanics, through the standard model and gravity, all the way to supergravity in d-space plus 2-time dimensions. I will describe how 2T-physics is consistent with 1T-physics in (d-1)-space plus 1-time dimensions, but also how it goes beyond 1T-physics, by making in principle a vast number of verifiable predictions that are systematically missed in 1T-physics, as well as providing new computational tools for physics.