Katrin Wendland

A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6

Abstract: We study the moduli space ℳ of N=(4,4) superconformal field theories with central charge c= 6. After a slight emendation of its global description we find the locations of various known models in the component of ℳ associated to K3 surfaces. Among them are the ℤ2 and ℤ4 orbifold theories obtained from the torus component of ℳ. Here, SO(4,4) triality is found to play a dominant role. We obtain the B-field values in direction of the exceptional divisors which arise from orbifolding. We prove T-duality for the ℤ2 orbifolds and use it to derive the form of ℳ purely within conformal field theory. For the Gepner model (2)4 and some of its orbifolds we find the locations in ℳ and prove isomorphisms to nonlinear σ models. In particular we prove that the Gepner model (2)4 has a geometric interpretation with Fermat quartic target space.

The overarching finite symmetry group of Kummer surfaces in the Mathieu group M24

A bstractIn view of a potential interpretation of the role of the Mathieu group M24 in the context of strings compactified on K3 surfaces, we develop techniques to combine groups of symmetries from different K3 surfaces to larger ‘overarching’ symmetry groups. We construct a bijection between the full integral homology lattice of K3 and the Niemeier lattice of type

Limits and Degenerations of Unitary Conformal Field Theories

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Mirror Symmetry on Kummer Type K3 Surfaces

, which is simultaneously compatible with the finite symplectic automorphism groups of all Kummer surfaces lying on an appropriate path in moduli space connecting the square and the tetrahedral Kummer surfaces. The Niemeier lattice serves to express all these symplectic automorphisms as elements of the Mathieu group M24, generating the ‘overarching finite symmetry group’

A K3 sigma model with Z_2^8:M_20 symmetry

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Crystallographic orbifolds: towards a classification of unitary conformal field theories with central charge c = 2

⋊ A7 of Kummer surfaces. This group has order 40320, thus surpassing the size of the largest finite symplectic automorphism group of a K3 surface by orders of magnitude. For every Kummer surface this group contains the group of symplectic automorphisms leaving the Kähler class invariant which is induced from the underlying torus. Our results are in line with the existence proofs of Mukai and Kondo, that finite groups of symplectic automorphisms of K3 are subgroups of one of eleven subgroups of M23, and we extend their techniques of lattice embeddings for all Kummer surfaces with Kähler class induced from the underlying torus.

Snapshots of Conformal Field Theory

In the present paper, degeneration phenomena in conformal field theories are studied. For this purpose, a notion of convergent sequences of CFTs is introduced. Properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of CFTs, which, as familiar from large volume limits of non- linear sigma models, can be regarded as commutative degenerations of the corresponding ‘‘quantum geometries’’. As an application, the large level limit of the A-series of unitary Virasoro minimal models is investigated in detail. In particular, its geometric interpretation is determined.

A twist in the M_{24} moonshine story

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 ℤN orbifold limits of K3. The resulting map gives an automorphism of order 4,8, or 12, respectively, on the smooth universal covering space 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.

Friendly Giant Meets Pointlike Instantons? On a New Conjecture by John McKay

A bstractThe K3 sigma model based on the

On the Geometry of Singularities in Quantum Field Theory

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