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Chern-Simons potentials of higher-dimensional Pontryagin densities
Onur Ayberk Çakmak, Özgür Sarıoğlu
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We develop a novel and systematic approach to computing the (2n-1)-form Chern-Simons potential given the Pontryagin density, i.e. the nᵗʰ Chern character, in arbitrary even dimensions D=2 n ≥2. Throughout we work with a generic affine connection, that results in a non-vanishing torsion in general, and allows for non-metricity, which accommodates the existence of non-trivial Chern characters and hence Pontryagin densities. We outline an algorithm, with its implementation as a code, which lets one to determine the Chern-Simons potential given the Pontryagin density in an arbitrary even dimension.
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