Naked singularities, branes and Chern-Simons couplings: The dark side of the 2+1 black hole

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Branes are naked singularities, analogous to linear or planar defects in crystals. Zero-branes in AdS spacetimes are "negative mass black holes", which can be generalized to higher-dimensional branes. When these solutions are endowed with angular momentum, the extremal spinning branes correspond to BPS states. On the other hand, the 2p-branes, spanning a (2p + 1)-dimensional worldsheet, provide a naturally coupling to CS field theories defined on a D-dimensional spacetime, with D > 2p + 1. In this picture, the field that lives in the D-dimensional spacetime, as well as the sources that couple to it are made out of the same stuff -an SO(D - 1,2) connection. The fact that on the brane the AdS group is necessarily broken down to SO(2p, 2), brings in a number of tensor fields that play the role of charged matter living on the brane.

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