Yang-Mills, Gravity, and 2D String Symmetries (original) (raw)

It is well known that by using the innite dimensional symmetries that issue from string theories, one can build 2D geometric eld theories. These 2D eld theories can be identied with gravitational and gauge anomalies that arise in the presence of background gauge and gravitational anomalies. In this work we consider the background elds as residuum from reducing higher dimensional eld theories to two dimensions. This implies a new relationship between string theory and eld theories. We identify the isotropy equations of the distinct orbits as the Gau's law constraints of a Yang-Mills theory coupled to a gravitational theory that has been evaluated on a two-dimensional manifold. We show explicitly how one may recover the higher dimensional theories and extract this new theory of gravity and its coupling to Yang-Mills theory. This gravitational theory is able to couple to Yang-Mills via a torsion-like term and yet maintain gauge invariance. Also this new theory of gravity suggest a natural distinction between cosmology and local gravitation. We comment on the analogue of Chern-Simons theory for dieomorphism, the vacuum structure of gravity, and also the possibility of extracting explicit realizations of distinct dierentiable structures in four dimensions.