Membrane duality revisited

Just as string T-duality originates from transforming field equations into Bianchi identities on the string worldsheet, so it has been suggested that M-theory U-dualities originate from transforming field equations into Bianchi identities on the membrane worldvolume. However, this encounters a problem unless the target space has dimension D = p + 1. We identify the problem to be the nonintegrability of the U-duality transformation assigned to the pull-back map. Just as a double geometry renders manifest the 0(D, D) string T-duality, here we show in the case of the M2-brane in D = 3 that a generalized geometry renders manifest the SL(3) x SL(2) U-duality. In the case of M2-brane in D=4, with and without extra target space coordinates, we show that only the GL(4, R) x R-4 subgroup of the expected SL(5, R) U-duality symmetry is realized. (C) 2015 The Authors. Published by Elsevier B.V.