Geometric Obstructions on Gravity

arXiv1912.11198MaRDI QIDQ6331723

Rodney Josué Biezuner, Yuri Ximenes Martins

Publication date: 23 December 2019

Abstract: These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author's paper arXiv:1808.09249. Some new information and results are also presented. Unlike the original work, here we try to give a more physical emphasis. In this sense, we present obstructions to realize gravity, modeled by the tetradic Einstein-Hilbert-Palatini (EHP) action functional, in a general geometric setting. In particular, we show that if spacetime has dimension $ngeq4$, then the cosmological constant plays no role in any "concrete geometries" other than Lorentzian. If $ngeq6$, then the entire EHP theory is trivial, meaning that Lorentzian geometry is (essentially) the only "concrete geometry" in which gravity (i.e, the EHP action functional) makes sense. Examples of "concrete geometries" include those locally modeled by group reductions $HhookrightarrowO(k;A)$ for some $k$ and some algebra $A$, so that Riemannian geometry, Hermitian geometry, K"ahler geometry and symplectic geometry, as well as Type II geometry, Hitchin's generalized complex geometry and $G_2$-geometry are included. We also study EHP theory in "abstract geometries", such as graded geometry (and hence supergeometry), and we show how the obstruction results extend to this context. We construct two theories naturally associated to EHP, which we call the geometric/algebraic dual of EHP, and we analyze the effect of the obstructions in these new theories. Finally, we speculate (and provide evidence for) the existence of a "universal obstruction condition".

This page was built for publication: Geometric Obstructions on Gravity

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6331723)