Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Abstract

In this thesis, we investigate hidden symmetries for the Maldacena-Wilson loop in N=4 super Yang-Mills theory, mainly focusing on its strong-coupling description as a minimal surface in $AdS_5$. In the discussion of the symmetry structure of the underlying string model, we highlight the role of the master symmetry which can be employed to construct all symmetries of the model. The algebra of these symmetries is worked out. For the concrete case of minimal surfaces in $AdS_5$, we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The discussion clarifies why previous attempts to transfer the deformations of minimal surfaces in $AdS_3$ to weak coupling were unsuccessful. We discuss several attempts to transfer the Yangian symmetry to weak or arbitrary coupling, but ultimately conclude that a Yangian symmetry of the Maldacena-Wilson loop seems not to be present. This is different for the natural supersymmetric generalizations of the Maldacena--Wilson loop, Wilson loops in superspace. Their one-loop expectation value is known to be Yangian invariant. We discuss the strong-coupling counterpart of this finding by considering minimal surfaces in the superspace of type IIB superstring theory in $AdS_5 \times S^5$. The comparison of the strong-coupling invariance derived here with the weak-coupling generators shows that the local term must depend on the coupling in a non-trivial way. Additionally, we show that the higher-level recurrences of the hypercharge generator, the so-called bonus symmetries, are present in all higher levels of the Yangian.