New modular invariants for N = 2 tensor products and four-dimensional strings

Abstract

The construction of modular invariant partition functions of tensor products of N = 2 superconformal field theories is clarified and extended by means of a recently proposed method using simple currents, i.e. primary fields with simple fusion rules. Apart from providing a conceptually much simpler way of understanding space-time and world-sheet supersymmetry projections in modular invariant string theories, this makes a large class of modular invariant partition functions accessible for investigation. We demonstrate this by constructing thousands of (2, 2), (1, 2) and (0, 2) string theories in four dimensions, including more than 40 new three generation models.