2025/05/06 by Lei, Yang, Zhang, Dong
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2505.03322
In this study, we investigate three-dimensional torsional Newton-Cartan (TNC) gravity by gauging the su(1,2)⊕u(1) algebra and construct its action using the Chern-Simons theory. This TNC exhibits novel features, including the fact that the gauge fields associated with both dilatation and rotation symmetries transform non-trivially under Galilean boosts. This theory also reproduces the Schrödinger gravity acquired by gauging the extended z=2 Schrödinger algebra arXiv:1604.08054 via a large speed of light (1/c)-expansion. In particular, we explain that the z=2 Lifshitz vacuum solution appearing in Schrödinger gravity is related to the null reduction of 4d Ω-background up to a conformal factor. Based on these results, we revisit the identification between the extended Schrödinger algebra and bosonic analogue of super BMS algebra arXiv:1905.13154. We interpret that this relation originates from the W3(2) algebra which acts as the bosonic analogue of N=2 superconformal algebra.