Landscape of Narain CFTs

Abstract

In this work, we investigate the AdS$_{3}$ gravitational bulk dual to an ensemble of Narain CFTs and their generalisations to establish bounds consistent with the Swampland program. Focusing on the AdS distance and finiteness conjectures, we show that the central charge of Narain CFTs forming the ensemble must be finite. Combining anomaly and unitary requirements, we derive an upper bound on the rank of the abelian U(1) gauge symmetries that can consistently couple to the AdS$_{3}$ gravity. We give explicit realisations of these constraints by determining the range of the Chern-Simons level $k^{G}$ corresponding to a bounded AdS$_{3}$ radius$.$ Accordingly, the Narain landscape is finite with a number of admissible CFTs constrained as $3/2\lesssim c\lesssim 10^{3}.$