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CALSCALE:GREGORIAN
PRODID:UW-Madison-Physics-Events
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SEQUENCE:3
UID:UW-Physics-Event-8149
DTSTART:20230222T190000Z
DTEND:20230222T203000Z
DTSTAMP:20260414T051300Z
LAST-MODIFIED:20230217T154053Z
LOCATION:Chamberlin 5280
SUMMARY:Geometry of Conformal Manifolds and the Inversion Formula\, Th
 eory Seminar (High Energy/Cosmology)\, Bruno Balthazar\, University of
  Chicago
DESCRIPTION:: Families of conformal field theories are naturally endow
 ed 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 Lorent
 zian inversion formulae\, which combine the operator content of the co
 nformal field theory into an analytic function. Analogously\, operator
 s of fixed dimension define bundles over the conformal manifold whose 
 curvatures can also be computed using inversion formulae. These result
 s relate curvatures to integrated four-point correlation functions whi
 ch are sensitive only to the behavior of the theory at separated point
 s. We apply these inversion formulae to derive convergent sum rules ex
 pressing the curvature in terms of the spectrum of local operators and
  their three-point function coefficients. We further show that the cur
 vature can smoothly diverge only if a conserved current appears in the
  spectrum\, or if the theory develops a continuum. We verify our resul
 ts explicitly in 2d examples.
URL:https://www.physics.wisc.edu/events/?id=8149
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