Analytic Bounds and Emergence of $\textrm{AdS}_2$ Physics from the Conformal Bootstrap

Understand

We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions.

• We introduce a new class of linear functionals acting on the conformal bootstrap equation.
• In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension.
• We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry.