/sci/ - Science & Math

>>11477720
Because the partition function [math]Z[/math] of a CFT on a symmetric [math]G[/math]-space [math]X[/math] naturally must be invariant under the mapping class group [math]\Gamma\subset G[/math] of [math]X[/math], hence can be expressed as a sum over automorphic forms. For instance, with [math]X = \mathbb{T}^2[/math], [math]G = SL(2,\mathbb{R})[/math] and [math]\Gamma=SL(2,\mathbb{Z})[/math] the modular group, this gets us the natural setting for a CFT partition function [math]Z[/math] on the moduli of the torus [math]\mathcal{M}_1[/math] as a section of a V-bundle over [math]\overline{\mathcal{M}}_1[/math] (modulo the action by Dehn twists [math]\mathbb{Z}[/math]), and we can in fact write [math]Z[/math] as a sum over modular forms such as the Jacobi theta.