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My question is about the M5-brane in M-theory. I would like to know whether the BPS states of the M5-brane worldvolume theory (especially the 1/2 BPS and 1/4 BPS ones) are independent of the topology of the worldvolume. By 1/2 BPS I mean states annihilated by 8 of the 16 supercharges of the M5-brane worldvolume theory superalgebra.

Say I compactify M-theory down to six dimensions on $T^5$, which is done in Dijkgraaf, Verlinde and Verlinde's 'BPS Quantization of the Five-brane' (http://arxiv.org/abs/hep-th/9604055), and following their procedure, I obtain the generic spacetime BPS states in terms of the 1/2 BPS states of the M5-brane worldvolume theory. Then, what happens to the spectrum of BPS states of the M5-brane worldvolume if I decompactify some of the dimensions of the $T^5$, e.g. to $T^2 \times R^3$?

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