Elliptic Genera of Complete Intersections in Weighted Projective Spaces

Abstract

We generalize the residue method of Ma–Zhou to compute the two-variable elliptic genera of smooth hypersurfaces and complete intersections in weighted projective spaces.

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups

“…The essential point of our paper is to carefully study the contribution from the zero-modes of the gauge multiplets. When the theory under consideration has a smooth geometric phase, our formula reproduces known mathematical results of the elliptic genus of complete intersections in toric varieties [16,17].…”

“…The essential point of our paper is to carefully study the contribution from the zero-modes of the gauge multiplets. When the theory under consideration has a smooth geometric phase, our formula reproduces known mathematical results of the elliptic genus of complete intersections in toric varieties [16,17].Let us first consider a U(1) gauge theory as an example. The most important zero-modes are the holonomy of the gauge group on the spacetime torus T 2 .…”

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories

“…See also [4,[30][31][32] Let us recall the mathematical computation first. A generalized genus in the sense of Hirzebruch of an almost complex manifold X is…”

New supersymmetric index of heterotic compactifications with torsion

“…This geometrical formula has been checked against (0, 2) Landau-Ginzburg results in [41], and directly compared with the results of supersymmetric localization for (2, 2) GLSMs in [24,25], building on previous works in the physical and mathematical literature [39,[54][55][56][57].…”