We revisit Narain conformal field theories from an algebraic perspective based on finite dimensional Lie algebras $\mathbf{ g}$ and representations $\mathcal{ R}_{ \mathbf{ g}}$, 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 $\mathcal{ M}_{ \mathbf{ g}}$ in terms of Lie algebraic data namely the Cartan matrix K$_{ \mathbf{ g}}$ and its inverse K$_{ \mathbf{ g}}^{ -1}$. 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 $(\mathrm{ c}_{ L},\mathrm{ c}_{ R})=(\mathrm{ s},% \mathrm{ r})$ with $s>r$ and highlight further features of the partition function Z$_{ \mathbf{ g}}^{ (r,r)}$.
Categories: hep-th