Abstract
We construct a Chern–Simons gauge theory for dg Lie and –infinity algebras on any one-dimensional manifold and quantize this theory using the Batalin–Vilkovisky formalism and Costello’s renormalization techniques. Koszul duality and derived geometry allow us to encode topological quantum mechanics, a nonlinear sigma model of maps from a –manifold into a cotangent bundle , as such a Chern–Simons theory. Our main result is that the effective action of this theory is naturally identified with the class of . From the perspective of derived geometry, our quantization constructs a projective volume form on the derived loop space that can be identified with the class.
Citation
Owen Gwilliam. Ryan Grady. "One-dimensional Chern–Simons theory and the $\hat{A}$ genus." Algebr. Geom. Topol. 14 (4) 2299 - 2377, 2014. https://doi.org/10.2140/agt.2014.14.2299
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