Abstract

Recently introduced connections between quantum codes and certain Narain CFT ’s let us write the partition functions of these CFT ’s in terms of objects that arise naturally from codes—the so-called `enumerator polynomials’. The recipe involved makes it easy to write down other modular-invariant functions that have an expansion in terms of u(1) characters (with positive integer coefficients); such functions are solutions to the modular bootstrap. However, we show that they cannot arise as partition functions of any 2d (unitary) CFT . That is, for these spectra, one cannot find a set of OPE coefficients consistent with crossing; but modular bootstrap constraints are not enough to rule them out. We consider only the simplest examples, keeping in mind that many more can be constructed.