Eisenstein Series and Instantons in String Theory

Abstract

In this thesis we review U-duality constraints on corrections to the type IIB supergravity effective action on torus compactifications. The U-duality invariant corrections are described by automorphic forms whose construction and Fourier expansion we explain. The latter enables us to extract physical information about instanton states in the theory. In particular, we discuss the first non-vanishing higher-derivative correction to the Einstein-Hilbert action in ten dimensions, for which there is a unique automorphic form incorporating all the perturbative and non-perturbative corrections in the string coupling constant. Acknowledgements I would especially like to give my sincere gratitude to my supervisor Daniel Persson for all his support, encouragement and wisdom. Thank you Daniel for all your help! It has been a great pleasure! Thank you Bengt E. W. Nilsson for all our discussions and for all the valuable knowledge you have shared. Joakim Edlund, thank you for proofreading this thesis and for providing such excellent insights. Also, thank you Axel Kleinschmidt and Philipp Fleig for your talks and helpful discussions. My thanks to the Department of Fundamental Physics for making me feel at home and last, but not least, thanks to my family and dear friends for their endless support and understanding. Content