Theory Seminar (High Energy/Cosmology)

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Events on Wednesday, February 22nd, 2023

Geometry of Conformal Manifolds and the Inversion Formula
Time: 1:00 pm - 2:30 pm
Place: Chamberlin 5280
Speaker: Bruno Balthazar, University of Chicago
Abstract: : Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Eu- clidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples.
Host: George Wojcik
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