Algebraic Realisation of the Zamolodchikov Metric in Narain Theories

ABSTRACT We revisit Narain conformal field theories ()from an algebraic perspective based on finite dimensional Lie algebras and representations , and show how the root and weight lattices can encode the momenta and subsequently the partition functions of Narain theories. In this framework, we construct a realisation of the Zamolodchikov metric of the moduli space in terms of Lie algebraic data, namely, the Cartan matrix and its inverse . Properties regarding the ensemble averaging of these CFTs and their holographic dual are also derived. Additionally, we discuss possible generalisations to NCFTs having dis‐symmetric central charges with , and highlight further features of the partition function .