Browsing by Author "Gandote, Sonagnon Eunice Edwige"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Gauge gravity dualities from group representation theory
    (2022) Gandote, Sonagnon Eunice Edwige
    This thesis considers two distinct problems. First we discuss scrambling and equilibration in N = 4 super Yang-Mills theory using operators that have a very large dimension, of order N2 . A basis for these operators, is provided by the so-called Gauss graph operators. The operators are labelled by a pair of Young diagrams and a graph. We characterize the typical graph and the dynamics associated to it. We show that the resulting dynamics is that of a fast scrambler. Our system equilibrates in a time scale given by t ∼ p λ where p is an order N number equal to the number of nodes in the graph and λ is the ’t Hooft coupling. Finally we use bilocal holography to explore the duality between the free O(N) vector model and higher spin gravity. We demonstrate a mapping between the CFT and the higher spin gravity that is determined by the symmetry of the problem. We then turn to a study of the geometry of this mapping. Using a specific code subspace, we demonstrate that bilocal holography reproduces the entanglement wedge reconstruction. We also make contact with ideas that have been influential in the holographic computation of entanglement entropy.
  • No Thumbnail Available
    Item
    Resurgence in the 1 2 BPS sector
    (2019) 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.