2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173611We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N=(2,2) 2D CFT's. 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.42pp., latex, 4 figures; v2: Several improvements in exposition have been addedHigh Energy Physics - Theorytext