# Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra

## TL;DR

This paper demonstrates how various non-relativistic symmetries in 2+1 dimensions can be derived from the Nappi-Witten algebra through algebraic expansions, enabling the construction of related Chern-Simons gravity theories.

## Contribution

It introduces a systematic method to obtain non-relativistic symmetry algebras from the Nappi-Witten algebra and constructs corresponding gravity theories.

## Key findings

- Extended Bargmann and Newton-Hooke algebras derived from Nappi-Witten algebra
- Two infinite families of non-relativistic symmetries identified
- Invariant tensors enable Chern-Simons gravity construction

## Abstract

We show that the Extended Bargmann and Newton-Hooke algebras in 2+1 dimensions can be obtained as expansions of the Nappi-Witten algebra. The result can be generalized to obtain two infinite families of non-relativistic symmetries, which include the Maxwellian Exotic Bargmann symmetry, its generalized Newton-Hooke counterpart, and its Hietarinta dual. In each case, the invariant bilinear form on the Nappi-Witten algebra leads to the invariant tensor on the expanded algebra, allowing one to construct the corresponding Chern-Simons gravity theory.