# Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

2705.pdf

(Publisher version), 311KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5677-1

##### 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.