Topological 4D gravity and gravitational defects

Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel topological 4D gravity given by Eq(5.1) with observables based on gravitational gauge field holonomies. The field action $S^{grav}_{4D}$ of this gravity has a gauge symmetry $SL(2,\mathbb{C})$ and reads also as the difference $S^{CWY_{L}}_{4D}-S^{CWY_{R}}_{4D}$ with 4D Chern-Simons field actions $S^{CWY_{L/R}}_{4D}$ given by left/right CWY theory Eq(3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS$_{3}$/CFT$_{2}$ correspondence with regard to the obtained topological 4D gravity.