Conformal manifolds: ODEs from OPEs

  • Connor BehanEmail author
Open Access
Regular Article - Theoretical Physics


The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this question, we compute perturbative corrections to several observables in an abstract CFT, starting with the beta function. This yields a sum rule that the theory must obey in order to be part of a conformal manifold. The set of constraints relating CFT data at different values of the coupling can in principle be written as a dynamical system that allows one to flow arbitrarily far. We begin the analysis of it by finding a simple form for the differential equations when the spacetime and theory space are both one-dimensional. A useful feature we can immediately observe is that our system makes it very difficult for level crossing to occur.


Conformal Field Theory Field Theories in Lower Dimensions Conformal and W Symmetry Nonperturbative Effects 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.C.N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookU.S.A.

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