Generalized Narain Theories Decoded: Discussions on Eisenstein series, Characteristics, Orbifolds, Discriminants and Ensembles in any Dimension

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these theories, thereby obtaining a large class of non-supersymmetric CFTs with exactly marginal deformations. We then discuss ensemble averages of such theories over their moduli space, and obtain a modular form associated with the quadratic form and an element of the discriminant group. The modular form can be written as a Poincare series, which contains novel invariants of lens spaces and suggests the interpretation of the holographic bulk as a theory of anyons.