Dimensional Worldvolume Research Articles

The energy spectrum of the membrane effective model for quantum black holes

We study first order fluctuations of a relativistic membrane in the curved background of a black hole. The zeroth-order solution corresponds to a spherical membrane tightly covering the event horizon. We obtain a massive Klein-Gordon equation for the fluctuations of the membrane's radial coordinate on the 2+1 dimensional world-volume. We finally suggest that quantization of the fluctuations can be related to black hole's mass quantization and the corresponding entropy is computed. This entropy is proportional to the membrane area and is related to the one-loop corretion to the thermodynamical entropy A H 4 . With regards to the membrane model for describing effectively a quantum black hole, we connect these results with previous work on critical phenomena in black hole thermodynamics.

Supermembranes and the signature of spacetime

We consider extended objects with s space and t time world-volume dimensions moving in a spacetime with S⩾ s space and T⩾ t time dimensions. The requirements of spacetime supersymmetry and world-volume fermionic gauge invariance severely restrict the possible values of S and T. If we furthermore insist that the transverse group SO( S − s, T− t) be compact to avoid ghosts, then t= T. The results may be interpreted as a set of superconformal field theories with s+ t⩽6 and N⩽8 whose superconformal groups are in one-to-one correspondence with those in Nahm's classification. Although the choice t = T = 1 is not uniquely singled out, it does seem to play a preferred role.

Supermembranes: the first fifteen weeks

There are four fundamental extended objects with d>2 world volume dimensions and D-dimensional spacetime supersymmetry: (d=3, D=11), (d=6, D=10), (d=4, D=6) and (d=3, D=4). A simultaneous dimensional reduction of the world-volume and the spacetime then yields four sequences of super-extended object which include the four classical Green-Schwarz superstrings (d=2, D=10, 6, 4 and 3) as special cases. The author discusses which of these models is likely to be quantum consistent and finishes with some speculations.