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Brown Bag Seminar | Geometry of Conformal Manifolds and the Inversion Formula

Bruno Balthazar (UChicago)
Wednesday, September 20, 2023
11:00 AM-12:00 PM
3481 Randall Laboratory Map
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 Euclidean 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.
Building: Randall Laboratory
Event Type: Lecture / Discussion
Tags: brown bag, Brown Bag Seminar, Physics
Source: Happening @ Michigan from Leinweber Center for Theoretical Physics, Department of Physics, HET Brown Bag Series, Leinweber Center for Theoretical Physics Seminars, Leinweber Center for Theoretical Physics Brown Bag Seminars