The AdS/CFT Correspondence, Integrability and Black Holes

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The project will investigate the quantum description of supersymmetric black holes in Anti de Sitter (AdS) space in the context of string theory, using the AdS/CFT correspondence to map these describe these objects in termsof a dual quantum field theory which flows to superconformal quantum mechanics in the IR. The aim is to compute a recently defined index for superconformal quantum mechanics which should (via AdS/CFT) count the microstates of such black holes (an important unsolved problem). In particular we will seek a relation between the integrable structures underlying the quantum mechanical model and the possible existence of infinite dimensional symmetries acting on the black hole horizon.