Correlators, Probabilities and Topologies in N=4 SYM

TL;DR

This paper explores how correlators in N=4 SYM relate to topological changes in the bulk AdS space, calculating transition probabilities involving gravitons and elucidating the role of non-trivial topologies through boundary correlators and Witten graphs.

Contribution

It introduces a novel framework connecting boundary correlators with bulk topology changes using gluing properties and Witten graphs in AdS/CFT correspondence.

Findings

Correlators encode topology-changing transition amplitudes.

Gluing of manifolds relates different boundary topologies.

Bulk topologies correspond to boundary correlator structures.

Abstract

We calculate transition probabilities for various processes involving giant gravitons and small gravitons in AdS space, using the dual N=4 SYM theory. The normalization factors for these probabilities involve, in general, correlators for manifolds of non-trivial topology which are obtained by gluing simpler four-manifolds. This follows from the factorization properties which relate CFT correlators for different topologies. These points are illustrated, in the first instance, in the simpler example of a two dimensional Matrix CFT. We give the bulk five dimensional interpretation, involving neighborhoods of Witten graphs, of these gluing properties of the four dimensional boundary CFT. As a corollary we give a simple description, based on Witten graphs, of a multiplicity of bulk topologies corresponding to a fixed boundary topology. We also propose to interpret the correlators as topology-changing transition amplitudes between LLM geometries.