Yangian symmetry of smooth Wilson loops in $ \mathcal{N}=4 $ super Yang-Mills theory

Abstract

We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N = 4 super Yang-Mills theory are invariant under a Yangian symmetry Y [psu(2, 2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS 5 × S 5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the N = 4 super Yang-Mills theory.

Master symmetry in the AdS 5 × S 5 pure spinor string

“…In [34] it was argued that the equivalence holds for any physical solution. With these results in mind, it is likely that one can extend the results of, for example, references [35,36] to the pure spinor string.…”

Wilson loops in N $$ \mathcal{N} $$ = 6 superspace for ABJM theory

“…Our focus is on the construction of null polygonal supersymmetric Wilson loops; however, in principle there should be no obstruction to defining a smooth supersymmetric Wilson loop, as done in ref. [13] for N = 4 super Yang-Mills.…”

“…The constant can be obtained by using the properties of the Wilson loop under different degenerations. 13 This form can be found for example in ref. [51, eqs.…”

Minimal area surfaces in AdSn+1 and Wilson loops

“…There is a large amount of work on the subject, see for example [6][7][8][9][10] and, in particular [11][12][13][14][15][16][17][18][19][20] for the circular Wilson loop, the most studied case. The main interest of this problem is its integrability properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The basic idea is that the computation of the Wilson loops in the strong coupling limit is translated into finding the area of the minimal surface ending on a boundary curve defined by the Wilson loop.…”