Abstract
The type IIA and type IIB supergravity actions in d = 10 dimensions are the lowenergy eective theories of type IIA and IIB string theory. In addition, the unique eleven dimensional supergravity theory is the lowenergy eective action of Mtheory. Higher order corrections to the lowenergy eective actions of these supergravity theories contain perturbative and nonperturbative eectsof the corresponding string theories and, as such, understanding the structure of the higher order terms provides an insight into the perturbative and nonperturbative formulations of string theory. The Uduality groups of type IIA/B string theory and Mtheory compactied on a torus to d < 10 dimensions puts powerful constraints on the higher derivative terms in the eective actions of these theories. In particular, the higher derivative terms in d = 10 􀀀 n dimensions are required to possess coecient functions that transform as En+1 (Z) automorphic forms. These automorphic forms are complex mathematical objects that encode all the perturbative and nonperturbative features of type II string theory and Mtheory compactied on an torus to d dimensions. We investigate the structure of the higher derivative terms and their associated automorphic forms in the eective actions of type IIA/B string theory and Mtheory. Constraints on automor
phic forms appearing in d dimensions by dimensional reduction of arbitrary higher derivative terms in the type IIA, type IIB and Mtheory eective actions to d dimensions are obtained. The behaviour of higher derivative terms in the d dimensional type II eective action in specic limits of various parameters is analysed. We derive a group theoretical interpretation for each limit. A general formula is given for a class of automorphic forms in these limits.
Date of Award  1 Jul 2012 

Original language  English 
Awarding Institution 

Supervisor  Neil Lambert (Supervisor) & Peter West (Supervisor) 