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

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

2001-02-19

arxiv.org/abs/hep-th/0102123v3

JHEP 0103:036,2001

Physics

High Energy Physics

High Energy Physics - Theory

Latex2e, 17 pages, JHEP.cls; v3: final version for JHEP, (iii) p.14 improved, plus cosmetics

Scientific paper

10.1088/1126-6708/2001/03/036

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 M-theory compactified on a torus $T^{d+1}$ 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 incorrect. It is argued 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. The exceptional correspondence $Sl(3)\times E_{6(6)}\subset E_{8(8)}$ offers the interesting prospect of solving the membrane small volume divergence and unifying membranes with five-branes.

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