Extremal N = (2, 2) 2D conformal field theories and constraints of modularity

Abstract

We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N = (2, 2) 2D CFTs. We show that such constraints have nontrivial implications for the existence of "extremal" N = (2, 2) conformal field theories. Applications to AdS3 supergravity and flux compactifications are addressed.