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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:20230330T035757Z
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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