Towards designer bootstrap by Miguel Paulos (LPENS Paris)

Bootstrap bounds for conformal field theories are often a double-edged sword: while they hold universally for vast classes of theories, this universality is also a source of frustration, as it is often difficult to constrain a specific theory.
I will explain how a detailed understanding of crossing equation available in 1d CFTs allow us to clarify why this occurs and how these difficulties may be palliated. In particular I will argue that an emergent picture suggests that specific theories can be pinpointed by a combination of additional sum rules and weak gap assumptions.