Correlators, Probabilities and Topologies in N=4 SYM

Details Correlators, Probabilities and Topologies in N=4 SYM Correlators, Probabilities and Topologies in N=4 SYM

2006-11-27

arxiv.org/abs/hep-th/0611290v2

JHEP 0703:072,2007

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX : 55 pages + Appendices (30 figures) version 2 : minor typos corrected + minor comments + acknowledgements added

Scientific paper

10.1088/1126-6708/2007/03/072

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.

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