Mirror Symmetry on Kummer Type K3 Surfaces

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.

27 pages, no figures; references added, typos and equation (28) corrected

References in corpus (3)

• Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
• Strings on Orbifold Lines
• Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau

Cited by in corpus (11)

• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• Symmetry-surfing the moduli space of Kummer K3s
• An Uplifting Discussion of T-Duality
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• Heterotic/type II Duality and Non-Geometric Compactifications
• Crepant resolutions of weighted projective spaces and quantum deformations
• D-Brane Charges in Gepner Models
• Moduli spaces and D-brane categories of tori using SCFT
• The Tanaka-Thomas's Vafa-Witten invariants via surface Deligne-Mumford stacks
• On explicit results at the intersection of the Z_2 and Z_4 orbifold subvarieties in K3 moduli space
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups