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Title:
Analytic conformal bootstrap
Speaker:
Abstract:
Conformal field theories (CFTs) in general dimension are central to our conceptual and quantitative understanding of quantum field theory and quantum gravity. They organize the space of couplings of quantum field theories by being the fixed points of renormalization group flows. Via holography, they offer the most precise description of quantum gravity available at the moment. At the same time, CFTs allow a completely rigorous non-perturbative definition in terms of the algebra of local operators. However, there is still no interacting conformal field theory above two dimensions and without supersymmetry, where any quantity of interest has been computed exactly. During the last decade, it was realized that unitarity (existence of a positive scalar product on the space of local operators) and crossing (associativity of the operator algebra) are very powerful constraints, raising the hope that at least some CFTs can be understood starting directly from the axioms for the operator algebra. I will review this so-called conformal bootstrap program, focusing on analytic results.
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