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  R^4 couplings, the fundamental membrane and exceptional theta correspondences

Pioline, B., Nicolai, H., Plefka, J., & Waldron, A. (2001). R^4 couplings, the fundamental membrane and exceptional theta correspondences. Journal of High Energy Physics, 2001(3): 036. doi:10.1088/1126-6708/2001/03/036.

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Pioline, Boris, Author
Nicolai, Hermann1, Author           
Plefka, Jan1, Author
Waldron, Andrew, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: This letter is an attempt to carry out a first-principle computation in M-theory using the point of view that the eleven-dimensional membrane gives the fundamental degrees of freedom of M-theory. Our aim is to derive the exact BPS $R^4$ couplings in toroidal compactifications of M-theory from the toroidal BPS membrane, by pursuing the analogy with the one-loop string theory computation. We exhibit an $Sl(3,Zint)$ modular invariance hidden in the light-cone gauge (but obvious in the Polyakov approach), and recover the correct classical spectrum and membrane instantons; the summation measure however is off. We argue that the correct membrane amplitude should be given by an exceptional theta correspondence lifting $Sl(3,Zint)$ modular forms to $exc(Zint)$ automorphic forms, generalizing the usual theta lift between $Sl(2,Zint)$ and $SO(d,d,Zint)$ in string theory, and outline the construction of such objects. The exceptional correspondence $Sl(3)imes E_6subset E_8$ offers the interesting prospect of solving the membrane small volume divergence and unifying membranes with five-branes.

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Language(s): eng - English
 Dates: 2001
 Publication Status: Issued
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 Identifiers: eDoc: 2705
DOI: 10.1088/1126-6708/2001/03/036
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Title: Journal of High Energy Physics
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Pages: - Volume / Issue: 2001 (3) Sequence Number: 036 Start / End Page: - Identifier: ISSN: 1126-6708