Mirror Symmetry on Kummer Type K3 Surfaces

TL;DR

This paper explores mirror symmetry in Kummer type K3 surfaces through geometric and conformal field theory methods, revealing automorphisms and the role of twist fields in orbifold limits.

Contribution

It provides a detailed analysis of mirror symmetry actions on singular fibers and their geometric counterparts in K3 surfaces, connecting conformal field theory with algebraic geometry.

Findings

Mirror symmetry induces automorphisms of order 4, 8, or 12 on the moduli space.

Explicit derivation of geometric counterparts of twist fields in orbifold CFTs.

Application of the McKay correspondence to interpret the results.

Abstract

We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable) singular fibers in elliptic fibrations of Z_N orbifold limits of K3. The resulting map gives an automorphism of order 4,8, or 12, respectively, on the smooth universal cover of the moduli space. We explicitly derive the geometric counterparts of the twist fields in our orbifold conformal field theories. The classical McKay correspondence allows for a natural interpretation of our results.