Bootstrapping Conformal Theories – conformalbootstrap

Recently, conformal bootstrap techniques have made great strides in tackling strongly-coupled problems in theoretical physics. Using this approach we have already produced world-leading predictions for three-dimensional Ising critical exponents and several other experimentally as well as theoretically important results.

In this proposal we aim to develop several novel bootstrap methods that will greatly enhance the predictive power of this approach. These new methods have the potential to revolutionize the field by reducing the bootstrap from a very difficult numerical problem to one of simple linear algebra. This would render the field much more accessible and allow for much faster exploration and development of new ideas. These new methods may also help shed light on tantalizing new features of the three-dimensional Ising model unearthed by existing bootstrap studies.

We will also explore several interesting classes of theories that have not yet been studied using the bootstrap such as two-dimensional theories with Virasoro symmetry and long-range theories in various dimensions. Finally we will apply the ideas of the bootstrap to holographic conformal field theories (in particular at finite temperature) in order to understand what underlies holographic dualities.