Non-relativistic three-dimensional supergravity theories and semigroup expansion method
Abstract
In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.
Cite
@article{arxiv.2010.01216,
title = {Non-relativistic three-dimensional supergravity theories and semigroup expansion method},
author = {Patrick Concha and Marcelo Ipinza and Lucrezia Ravera and Evelyn Rodríguez},
journal= {arXiv preprint arXiv:2010.01216},
year = {2021}
}
Comments
v1, 37 pages