Conformal Manifolds with Boundaries or Defects

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We discuss conformal manifolds for conformal field theories with boundaries or defects.

• Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions that need to be satisfied for the existence of marginal couplings.
• We present several explicit examples where we confirm that $\beta$-functions vanish using a position space regularization, differential regularization.
• Where possible, we confirm that our $\beta$-function results agree with the existing literature.