Landscape of Narain CFTs

TL;DR

This paper explores the landscape of Narain conformal field theories (CFTs) and their gravitational duals in AdS3, establishing bounds on their parameters to ensure consistency with the Swampland conjectures, and demonstrating the finiteness of the Narain landscape.

Contribution

It provides the first systematic bounds on the parameters of Narain CFTs based on Swampland criteria, linking anomaly, unitarity, and gravitational constraints.

Findings

The central charge of Narain CFTs must be finite.

An upper bound on the U(1) gauge symmetry rank is derived.

The number of admissible Narain CFTs is constrained between approximately 2 and 1000.

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 $3/2\lesssim c\lesssim 10^{3}.$