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 O(D,D) string T-duality, here we show in the case of the M2-brane in D=3 that a generalised geometry renders manifest the SL(3)×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)⋉R4 subgroup of the expected SL(5,R) U-duality symmetry is realised.

Membrane duality revisited

Percacci, Roberto;
2015-01-01

Abstract

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 O(D,D) string T-duality, here we show in the case of the M2-brane in D=3 that a generalised geometry renders manifest the SL(3)×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)⋉R4 subgroup of the expected SL(5,R) U-duality symmetry is realised.
2015
901
1
21
10.1016/j.nuclphysb.2015.10.003
Duff, M. J.; Lu, J. X.; Percacci, Roberto; Pope, C. N.; Samtleben, H.; Sezgin, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15823
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