Resurgence in the 1 2 BPS sector
Gandote, Sonagnon Eunice Edwige
We study matrix models as a toy model for N = 4 Super Yang-Mills (SYM) theory which is a quantum eld theory. In particular we are interested in the gauge/gravity duality which conjectures an equivalence between N = 4 SYM and IIB string theory on AdS5 S5. We discuss the planar 't Hooft limit where we x = g2Y MN while taking N ! 1. In this limit we nd 1=N2 in the matrix model is equivalent to ~ of the string theory. When we study the N dependence of ribbon graphs, we nd that the 1 N expansion in the gauge theory can be interpreted as a sum over surfaces suggestive of the perturbation expansion of a closed string theory. We then consider a non-planar but large N limit, allowing us to discuss the giant graviton. We nd that the group representation theory of the symmetric group and unitary group organizes the physics of giant gravitons. We compute two, three and multi point functions of giant graviton operators. The large N expansion of giant graviton correlators is considered. Giant gravitons are described using operators with a bare dimension of order N. In this case the usual 1=N expansion is not applicable and there are contributions to the correlator that are non-perturbative in character. The machinery needed to determine the non-pertubative physics form the pertubative contributions is the origin of the term resurgence. By writing the (square of the) correlators in terms of the hypergeometric function 2F1(a; b; c; 1), we clarify the structure of the 1=N expansion.
A dissertation submitted to the University of the Witwatersrand in ful lment of the requirements for candidacy for the degree of Master of Science. Johannesburg, 2019