Compact Conformal Manifolds

Understand

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric).

• Supersymmetry guarantees that such manifolds are Kahler, and so the simplest possible non-trivial compact conformal manifold in this set of geometries is a complex one-dimensional projective space.
• We show that such a manifold is indeed realized and give a general prescription for constructing complex N-dimensional projective space conformal manifolds as certain small N=2->N=1 breaking deformations of strongly interacting N=2 SCFTs.
• In many cases, our prescription reduces the construction of such spaces to a study of the N=2 chiral ring.