Triangle Seminars

Abstract:
Maximally supersymmetric string theory compactified on d-dimensional torus is invariant under the non-perturbative U-duality groups E_{d+1}(Z). These duality groups are the discrete version over the integers of the real split forms of the simply laced lie groups of rank d. The interactions of the theory are given by automorphic function under E_{d+1}(Z), given in the simplest cases by the residue of maximal parabolic Eisenstein series. The dimensional reduction of the theory to three dimensions gives rise to the duality group E_8 from which all BPS couplings in higher dimensions can be extracted.

We will present the construction of the automorphic form relevant for the supersymmetric protected BPS interactions in the low-energy expansion of maximal supersymmetric effective action.

We will show that the support of the non-vanishing Fourier coefficients for these automorphic form is given by the expected BPS conditions one can derive from the supersymmetric conditions.