2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123401We propose a localization formula for the chiral de Rham complex generalizing the well-known localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the non-linear beta-gamma system as a gauge theory. For abelian gauge groups we are in the realm of toric geometry. Including the b-c system, the formula reproduces the known results for the elliptic genus of toric varieties. We compute the partition function of several models.52 pages, Latex, no figuresHigh Energy Physics - Theorytext