On some feature and application of the Faddeev formulation of gravity

In the Faddeev formulation of gravity, the metric is regarded as composite field, bilinear of $d = 10$ 4-vector fields. A unique feature is that this formulation admits the discontinuous fields. On the discrete level, when spacetime is decomposed into the elementary 4-simplices, this means that the 4-simplices may not coincide on their common faces, that is, be independent. We apply this to the particular problem of quantization of the surface regarded as that composed of virtually independent elementary pieces (2-simplices). We find the area spectrum being proportional to the Barbero-Immirzi parameter $\gamma$ in the Faddeev gravity and described as a sum of spectra of separate areas. According to the known in the literature approach, we find that $\gamma$ exists ensuring Bekenstein-Hawking relation for the statistical black hole entropy for arbitrary $d$, in particular, $\gamma = 0.39...$ for genuine $d = 10$.