Chern-Simons potentials of higher-dimensional Pontryagin densities

TL;DR

This paper introduces a systematic method and algorithm for computing Chern-Simons potentials from Pontryagin densities in arbitrary even dimensions, accommodating torsion and non-metricity.

Contribution

It presents a novel algorithm and code implementation for deriving Chern-Simons potentials from Pontryagin densities in any even dimension, considering general affine connections.

Findings

Developed a systematic approach for arbitrary even dimensions.

Implemented an algorithm as a code for practical computation.

Accommodated torsion and non-metricity in the calculations.

Abstract

We develop a novel and systematic approach to computing the $(2n-1)$-form Chern-Simons potential given the Pontryagin density, i.e. the $n^{\text{th}}$ Chern character, in arbitrary even dimensions $D=2 n \geq 2$. 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.