Non-relativistic three-dimensional supergravity theories and semigroup expansion method

• Main Authors: Patrick Concha, Marcelo Ipinza, Lucrezia Ravera, Evelyn Rodríguez
• Format: Article
• Language: English
• Published: SpringerOpen 2021-02-01
• Series: Journal of High Energy Physics
• Subjects: Chern-Simons Theories; Supergravity Models; Gauge Symmetry; Classical Theories of Gravity
• Online Access: https://doi.org/10.1007/JHEP02(2021)094

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.