Abstract
Using our previous construction of Eisenstein-like automorphic forms we derive formulae for the perturbative and non-perturbative parts for any group and representation. The result is written in terms of the weights of the representation and the derivation is largely group theoretical. Specialising to the En+1 groups relevant to type II string theory and the representation associated with node n+1 of the En+1 Dynkin diagram we explicitly find the perturbative part in terms of String Theory variables, such as the string coupling g(d) and volume V-n. For dimensions seven and higher we find that the perturbation theory involves only two terms. In six dimensions we construct the SO(5, 5) automorphic form using the vector representation. Although these automorphic forms are generally compatible with String Theory, the one relevant to R-4 involves terms with g(d)(-6) and so is problematic. We then study a constrained SO(5, 5) automorphic form, obtained by summing over null vectors, and compute its perturbative part. We find that it is consistent with String Theory and makes precise predictions for the perturbative results. We also study the unconstrained automorphic forms for E-6 in the 27 representation and E-7 in the 133 representation, giving their perturbative part and commenting on their role in String Theory.
Original language | English |
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Article number | 098 |
Journal | Journal of High Energy Physics |
Volume | 2010 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2010 |