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Asymmetric orbifolds and quaternionic automorphic functions

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NC2W02 - Crossing the bridge: New connections in number theory and physics

The string theory low energy effective action has been extensively studied in Minkowski vacua with N=4 and 8 supersymmetries. The couplings are automorphic functions of the moduli by U-duality. Much less is known about string theory vacua with N=6 supersymmetries that are realised as asymmetric orbifolds. We will argue that there are two distinct N=6 string theory vacua  and we determine the U-duality group of symmetry. Using perturbative string theory computations and constraints from supersymmetry we derive the exact protected couplings of the low energy effective action. They are automorphic functions on half-spaces of quaternions bases respectively on the Hurwitz and the Eisenstein quaternion rings.

This talk is part of the Isaac Newton Institute Seminar Series series.

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