Symmetries of Maldacena-Wilson Loops from Integrable String Theory

TL;DR

This thesis explores hidden symmetries of Maldacena-Wilson loops in N=4 super Yang-Mills theory at strong coupling, focusing on the role of master and Yangian symmetries in minimal surfaces within AdS5, and their potential transfer to scattering amplitudes and weak coupling.

Contribution

It introduces the concept of master symmetry in the string model, analyzes its algebra, and investigates the transfer of these symmetries to scattering amplitudes and weak coupling regimes.

Findings

Master symmetry can generate all symmetries of the string model.

Yangian symmetry appears not to transfer to weak coupling for Maldacena-Wilson loops.

Supersymmetric Wilson loops in superspace are Yangian invariant at one loop.

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.