A glimpse into the conformal bootstrap program
I will make an introduction into the conformal bootstrap program of solving quantum field theories with conformal symmetry, first proposed by Polyakov et al. in the 1970s. In the last decade this program has seen a resurgence of interest, due to the impressive advances in numerical computation of low-lying operator dimensions for important physical theories (such as 3d Ising model), achieved by using semidefinite programming techniques. I will discuss the links of bootstrap to harmonic analysis and representation theory, a possibility of its rigorous mathematical formulation and some intriguing open questions.
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