A model for complex analytic equivariant elliptic cohomology from quantum field theory

Abstract

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge fields and $\mathcal{N}=(0,1)$ supersymmetry. We also consider a theory of free fermions valued in a representation whose partition function is a section of a determinant line bundle. We identify this section with a cocycle representative of the (twisted) equivariant elliptic Euler class of the representation. Finally, we show that the moduli stack of $U(1)$-gauge fields carries a multiplication compatible with the complex analytic group structure on the universal (dual) elliptic curve, with the Euler class providing a choice of coordinate. This provides a physical manifestation of the elliptic group law central to the homotopy-theoretic construction of elliptic cohomology.

arXiv commentSignificant updates informed by the de Rham model in 1908.02868

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Cited by in corpus (3)

• Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety
• Quantizing Derived Mapping Stacks
• Topological Mathieu Moonshine