Abstract
A quadratic Leibniz algebra gives rise to a canonical Yang-Mills type functional over every space-time manifold. The gauge fields consist of 1-forms taking values in and 2-forms with values in the subspace generated by the symmetric part of the bracket. If the Leibniz bracket is antisymmetric, the quadratic Leibniz algebra reduces to a quadratic Lie algebra, , and becomes identical to the usual Yang-Mills action functional. We describe this gauge theory for a general quadratic Leibniz algebra. We then prove its (classical and quantum) equivalence to a Yang-Mills theory for the Lie algebra to which one couples massive 2-form fields living in a -representation. Since in the original formulation the -fields have their own gauge symmetry, this equivalence can be used as an elegant mass-generating mechanism for 2-form gauge fields, thus providing a “higher Higgs mechanism” for those fields.
- Received 4 April 2019
DOI:https://doi.org/10.1103/PhysRevD.99.115026
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society