On search for the M-Theory Lagrangian

We present a starting point for the search for a Lagrangian density for M-Theory using characteristic classes for flat foliations of bundles.Comment: Latex, 5 pages, no figure

Geometry of the non-Abelian 2-index potential and twisted de Rham cohomology

It is found that the 2-index potential in nonabelian theories does not behave geometrically as a connection but that, considered as an element of the second de Rham cohomology group twisted by a flat connection, it fits well with all the properties assigned to it in various physical contexts. We also prove some results on the Euler characteristic of the twisted de Rham complex. Finally, provided that some conditions are satisfied, we propose a non-Abelian generalisation of S-duality.Comment: 11 pages, Latex; to appear in Repts. on Math. Phy

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

On Polyakov's basic variational formula for loop spaces

We use the homological algebra context to give a more rigorous proof of Polyakov's basic variational formula for loop spaces.Comment: Latex, 17 pages, no figure