Aspects of gauge/string theory duality: BMN correspondence and MHV rules

Abstract

One of the most striking examples of duality correspondence between gauge theories and string theories is the AdS/CFT duality. It relates the type IIB superstring theory on AdS5 x 5 5 to 4-dimensional N = 4 Yangs Mills in its superconformal phase. However, the quantisation of string theory on curved backgrounds appears to be notoriously difficult rendering direct tests of the conjecture elusive. One way to circumvent this problem is by taking the Penrose limit of the AdS5 x 5 5 geometry to obtain the pp-wave background where string theory is soluble. The corresponding limit in gauge theory is to restrict to particular class of" long" operators called BMN operators. It is this correspondence we study in the first part of this thesis. In particular, we provide with a number of rigorous tests of the BMN correspondence beyond the supergravity limit, that probe the truly quantum realm of string theory. By exploring the correspondence, we learn how the correspondence is realised and how the 3-string amplitudes can be obtained purely from perturbative gauge theory calculations for almost all species of string excitations. We also clarify the role of the Z2 symmetry the pp-wave background possesses and discuss the consequences this symmetry has on the choice of the 3-string vertex. There is another type of duality which relates the same N = 4 SYM to a different string theory. This is a weak-to-weak coupling duality recently proposed by Witten. It states that tree level amplitudes of N = 4 SYM can be reproduced by integrating over the moduli space of certain D-instantons in open topological B-model in super-twistor space. This duality has inspired a novel diagrammatic method for calculating