Elliptic genera and real Jacobi forms

Abstract

We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional N} = (2, 2) supersymmetric theories. They arise in a family labeled by two integers N and k which determine the central charge of the infrared fixed point through the formula c = 3N (1 + 2N/k). We decompose the real Jacobi form into a mock modular form and a term arising from the continuous spectrum of the conformal field theory. For a given N and k we argue that the Jacobi form represents the elliptic genus of a theory defined on a 2N dimensional linear dilaton background with U(N) isometry, an asymptotic circle of radius √ kaPrime; and linear dilaton slope N√2/k. We also present formulas for the elliptic genera of their orbifolds. © 2014 SISSA.