c=2 Rational Toroidal Conformal Field Theories via the Gauss Product

We find a concise relation between the moduli $τ, ρ$ of a rational Narain lattice $Γ(τ,ρ)$ and the corresponding momentum lattices of left and right chiral algebras via the Gauss product. As a byproduct, we find an identity which counts the cardinality of a certain double coset space defined for isometries between the discriminant forms of rank two lattices.

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