Nat Levine (UvA) - Bounds on the convexity of scaling dimensions over conformal manifolds

by Nat Levine (University of Amsterdam)

Wednesday 19 Nov 2025, 15:15 → 16:15 Europe/Stockholm

92110 (Ångströmlaboratoriet)

If a conformal field theory has exactly marginal operators, then its scaling dimensions are functions over a 'conformal manifold' of couplings. We propose new bounds on these functions due to unitarity. Specifically, the dimension of the lightest scalar with any given quantum numbers is subject to an upper bound on its convexity over the conformal manifold. Similar bounds apply to the sum of the lightest n scalars (for any n) and to the lightest unprotected scalar. The bounds are derived using​ conformal perturbation theory, positivity assumptions, and an OPE truncation in a particular kinematic region. The latter is justified by a careful estimate of the truncated terms, leading to error bars for the bounds. The bounds are tested in a simple 2d example.