Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity

TL;DR

This paper investigates how modularity constraints on the elliptic genus of N=(2,2) 2D conformal field theories limit their spectra, with implications for extremal theories, AdS3 supergravity, and flux compactifications.

Contribution

It demonstrates the nontrivial restrictions imposed by modularity on the spectrum of N=(2,2) 2D CFTs and explores their implications for extremal theories and related physical models.

Findings

Modularity constrains the spectrum of primary fields in N=(2,2) 2D CFTs.

Constraints have significant implications for the existence of extremal conformal field theories.

Applications to AdS3 supergravity and flux compactifications are discussed.

Abstract

We 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.