One-dimensional Chern-Simons theory and the $\hat{A}$ genus

Details One-dimensional Chern-Simons theory and the $\hat{A}$ genus One-dimensional Chern-Simons theory and the $\hat{A}$ genus

2011-10-16

arxiv.org/abs/1110.3533v1

Mathematics

Quantum Algebra

64 pages, figures

Scientific paper

Recently, Kevin Costello constructed a 2-dimensional conformal field theory from a K\"ahler manifold X whose partition function over an elliptic curve recovers the elliptic genus of X. Inspired by this work, we construct the analogous 1-dimensional field theory, which is a nonlinear sigma model of maps from a circle into a smooth manifold $T^\ast X$. Our main result is that the partition function recovers the $\hat{A}$ genus of $X$.

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