nLab Bismut-Chern character

Idea

A version of the Chern character on free loop space.

Related concepts

• superconnection

• free loop space

References

The original article:

• Jean-Michel Bismut, Index Theorem and Equivariant Cohomology on the Loop Space, Comm. in Math. Phys. 98 (1985) 213-237 [doi:10.1007/BF01220509, euclid]

Further development:

• Fei Han, Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character [arXiv:0711.3862

• Fei Han, Varghese Mathai, Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality, Commun. Math. Phys. 337 (2015) 127-150 [arXiv:1405.1320, doi:10.1007/s00220-014-2270-z]

reviewed in:

• Varghese Mathai, T-duality for loop spaces, or equivalently for the 1D sigma model, talk at M-Theory and Mathematics 2023, NYU Abu Dhabi (Jan 2023) [web]