Quantized Topological 2-form Gravity
  We develop a perturbation theory of four-dimensional topological 2-form gravity without cosmological constant.   A 2-form and an $SU(2)$ connection 1-form are used as fundamental variables instead of metric.   There is no quantum correction from two-loop and higher orders in covariant gauge, in Landau gauge and in background covariant gauge.   We improve naive dimensional regularization and calculate an exact quantum correction at one-loop order.   We observe that the renormalizability depends on gauge choice in topological 2-form gravity.   It is unrenormalizable in the covariant gauge and in the background covariant gauge.   On the other hand in the Landau gauge, we obtain finite but $SU(2)$ non-covariant quantum corrections.   There may exist anomaly for the $SU(2)$ gauge symmetry.   (Talk given by A. Nakamichi at the Workshop on General Relativity and Gravitation held at Tokyo University, January 17-20,1994.) 
Tomoyuki Inui, Akika Nakamichi