Exceptional Operators in N=4 super Yang-Mills

We consider one particularly interesting class of composite gauge-invariant operators in N=4 super Yang-Mills theory. An exceptional feature of these operators is that in the Thermodynamic Bethe Ansatz approach the one-loop rapidities of the constituent magnons are shown to be exact in the 't Hooft coupling constant. This is used to propose the mirror TBA description for these operators. The proposal is shown to pass several non-trivial checks.Comment: 40 pages, 2 figures, 1 attached Mathematica noteboo

Multi-particle finite-volume effects for hexagon tessellations

Correlation functions of gauge-invariant composite operators in N = 4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual (\u201cmirror\u201d) magnons. We consider this problem for five-point functions of protected operators. At one-loop in the \u2019t Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem