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arXiv · 1509.02915

Membrane Duality Revisited

M. J. Duff·J. X. Lu·R. Percacci·C. N. Pope·H. Samtleben·E. Sezgin
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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 $SL(3) \times SL(2)$ U-duality. In the case of M2-brane in $D=4$, with and without extra target space coordinates, we show that only the ${\rm GL}(4,R)\ltimes R^4$ subgroup of the expected $SL(5,R)$ U-duality symmetry is realised.

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M. J. Duff, J. X. Lu, R. Percacci, C. N. Pope, H. Samtleben, E. Sezgin. 2015-09-09. Membrane Duality Revisited. https://doi.org/10.1016/j.nuclphysb.2015.10.003

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