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

TL;DR

This paper establishes a concise relation between moduli of rational Narain lattices and their chiral algebra momentum lattices using the Gauss product, revealing new identities related to lattice isometries.

Contribution

It introduces a novel relation connecting moduli of rational Narain lattices with chiral algebra momentum lattices through the Gauss product, and derives an identity for counting isometries of discriminant forms.

Findings

Derived a relation between moduli and momentum lattices using the Gauss product.

Established an identity for counting isometries between discriminant forms.

Connected lattice theory with algebraic structures in conformal field theories.

Abstract

We find a concise relation between the moduli $\tau, \rho$ of a rational Narain lattice $\Gamma(\tau,\rho)$ 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.