Landscape of Narain CFTs

In this work, the gravitational bulk dual to an ensemble of Narain CFTs and their generalisations is investigated to establish bounds consistent with the Swampland program. Focusing on the AdS distance and finiteness conjectures, the central charge of Narain CFTs forming the ensemble is shown to be finite. Combining anomaly and unitary requirements, an upper bound on the rank of the abelian U(1) gauge symmetries that can consistently couple to the gravity is derived. Explicit realisations are given of these constraints by determining the range of the Chern–Simons level corresponding to a bounded radius. Accordingly, the Narain landscape is finite with a number of admissible CFTs constrained as .