1995/10/19 by HoSeong La, La, HoSeong · 1 citation
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9510147
25 pages, LaTeX
arxiv created 1995/10/19 · arxiv updated 2009/11/30
Area preserving diffeomorphisms of a 2-d compact Riemannian manifold with or without boundary are studied. We find two classes of decompositions of a Riemannian metric, namely, h- and g-decomposition, that help to formulate a gravitational theory which is area preserving diffeomorphism (SDiffM-) invariant but not necessarily diffeomorphism invariant. The general covariance of equations of motion of such a theory can be achieved by incorporating proper Weyl rescaling. The h-decomposition makes the conformal factor of a metric SDiffM-invariant and the rest of the metric invariant under conformal diffeomorphisms, whilst the g-decomposition makes the conformal factor a SDiffM scalar and the rest a SDiffM tensor. Using these, we reformulate Liouville gravity in SDiffM invariant way. In this context we also further clarify the dual formulation of Liouville gravity introduced by the author before, in which the affine spin connection is dual to the Liouville field.