A family of SCFTs hosting all "very attractive" relatives of the (2)^4 Gepner model

TL;DR

This paper constructs a family of superconformal field theories related to certain K3 surfaces, including the (2)^4 Gepner model, using orbifold techniques and dualities, expanding understanding of their geometric and conformal structures.

Contribution

It introduces a four-parameter family of SCFTs associated with quartic K3 surfaces, connecting geometric models with conformal field theories through orbifold and duality methods.

Findings

Constructed a four-parameter family of SCFTs for quartic K3 surfaces.

Identified all 'very attractive' K3 surfaces within this family.

Related the (2)^4 Gepner model to complex structure deformations.

Abstract

This work gives a manual for constructing superconformal field theories associated to a family of smooth K3 surfaces. A direct method is not known, but a combination of orbifold techniques with a non-classical duality turns out to yield such models. A four parameter family of superconformal field theories associated to certain quartic K3 surfaces in CP^3 is obtained, four of whose complex structure parameters give the parameters within superconformal field theory. Standard orbifold techniques are used to construct these models, so on the level of superconformal field theory they are already well understood. All "very attractive" K3 surfaces belong to the family of quartics underlying these theories, that is all quartic hypersurfaces in CP^3 with maximal Picard number whose defining polynomial is given by the sum of two polynomials in two variables. A particular member of the family is the (2)^4 Gepner model, such that these theories can be viewed as complex structure deformations of (2)^4 in its geometric interpretation on the Fermat quartic.