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.