The book discusses hidden symmetries in the Anti-de Sitter conformal field theory (AdS CFT)
duality. This duality is a modern concept that asserts an exact duality between conformally
invariant quantum field theories and string theories in higher dimensional Anti-de Sitter
spaces and in this way provides a completely new tool for the study of strongly coupled
quantum field theories.In this setting the book focuses on the Wilson loop an important
observable in four-dimensional maximally supersymmetric gauge theory. The dual string
description using minimal surfaces enables a systematic study of the hidden symmetries of the
loop. The book presents major findings including the discovery of a master symmetry for
strings in general symmetric spaces its relation to the Yangian symmetry algebra and its
action on the minimal surfaces appearing in the dual string description of the Wilson loop.
Moreover it clarifies why certain symmetries are not present on thegauge theory side for
purely bosonic Wilson loops and lastly how the supersymmetrization of the minimal surface
problem for type IIB superstrings can be undertaken. As such it substantially increases our
understanding and use of infinite dimensional symmetries occurring in the AdS CFT
correspondence.
