Linking Chains Together String Bits and the Bethe Ansatz

Sammanfattning: This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS5 x S5 and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS5 rotate quickly around the equator of the S5 and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order.Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers from the problem of fermion doubling, a general pathology of fermions on a lattice. In paper II we show how to adjust the theory in order to avoid this problem and, in fact, use the fermion doubling to our advantage. The second part of the thesis studies the low energy behaviour of SU(2) Yang-Mills theory in 4 space-time dimensions. In paper I we perform numerical calculations on an effective action for this theory. We propose the existence of a knotted trajectory within the dynamics of this effective action.