This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Conformal field theories have many applications ranging
from continuous phase transitions in Statistical Mechanics to models of beyond
the Standard Model physics in Particle Physics.
In this talk, I will explain another remarkable
application: some conformal field theories can be used to define and study
Quantum Gravity.
I will also try to give a brief summary of some of the
main ideas being discussed at the conference "Back to the Bootstrap II".
There is strong theoretical evidence that black holes have a finite thermodynamic entropy equal to one quarter the area A of the horizon. Providing a microscopic derivation of the entropy of the horizon is a major task for a candidate theory of quantum gravity. Loop quantum gravity has been shown to provide a geometric explanation of the finiteness of the entropy and of the proportionality to the area of the horizon. The microstates are quantum geometries of the horizon.
Shape Dynamics first arose as a theory of particle interactions formulated without any of Newton's absolute structures. Its fundamental arena is shape space, which is obtained by quotienting Newton's kinematic framework with respect to translations, rotations and dilatations. This leads to a universe defined purely intrinsically in relational terms. It is then postulated that a dynamical history is determined by the specification in shape space of an initial shape and an associated rate of change of shape. There is a very natural way to create a theory that meets such a requirement.
Majorana disappeared under mysterious circumstances in 1938 and the particle that bears his name remains elusive to experiments. There is growing interests in realizing the Majorana bound state in the Laboratory because it is expected to possess unusual properties such as non-abelian statistics. I shall discuss various proposals to produce Majorana bound states and the associated topological superconductors which support them.
There has been some significant recent progress on the long-standing problem of identifying the conditions under which equilibrium statistical mechanics can arise from an exact quantum mechanical treatment of the dynamics. I will give an overview of this progress, describing in particular how random matrix models and the associated concentration of measure phenomena imply that equilibration is generic even for the closed system evolution of pure quantum states.
I will describe a new numerical effort to solve Einstein gravity in 5-dimensional asymptotically Anti de Sitter spacetimes (AdS). The motivation is the gauge/gravity duality of string theory, with application to scenarios that on the gravity side are described by dynamical, strong-field solutions. For example, it has been argued that certain properties of the quark-gluon plasma formed in heavy-ion collisions can be modeled by a conformal field theory, with the dual description on the gravity side provided by the collision of black holes.
The covariant formulation of loop quantum gravity has developed strongly during the last few years. I summarize the current definition of the theory and the results that have been proven. I discuss what is missing towards of the goal of defining a consistent quantum theory whose classical limit is general relativity.
Mass, a concept familiar to all of us, is also
one of the deepest
mysteries in nature. Almost all of the mass in the
visible universe,
you, me and any other stuff that we see around us, emerges from a
quantum field theory, called QCD, which has a completely negligible
microscopic mass content. How does QCD and the family of
gauge
theories it belongs to generate a mass?
This class of non-perturbative problems remained largely elusive despite much