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Abstract |
I will discuss properties of 1D quantum theories with SL(2) invariance from the point of view of the conformal bootstrap. The simplest solutions of the 1D bootstrap equation correspond to free fields propagating in AdS_2. Small deformations around these solutions are severely constrained by the bootstrap equation and can be understood in terms of local renormalizable interactions of the fields in AdS_2. The 1D bootstrap equation thus allows us to compute Witten diagrams in AdS_2 with relative ease. These results are known in higher d but require a new technique in 1D, namely the construction of analytic extremal functionals. Time permitted, I will show how the same technique provides a connection between the modular bootstrap and the recent progress on the sphere-packing problem. |
