Supersymmetric Wilson loops at two loops

Abstract

We study the quantum properties of certain BPS Wilson loops in N = 4 supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on S 3 with a fraction of supersymmetry. When restricted to S 2 , their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM 2 on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

Precision calculation of 1/4-BPS Wilson loops in AdS5×S5

“…The family of 1/4-BPS latitude Wilson loops falls under the more general class of 1/8-BPS Wilson loops with arbitrary shape on a two-sphere introduced in [15,24,25] and studied in [26]. There are strong evidences that they localize into Yang-Mills theory on S 2 in the zeroinstanton sector [15,[26][27][28] and their vacuum expectation values are therefore related to the 1/2-BPS one by a simple rescaling. As originally argued in [18] the expectation value of such latitude Wilson loops is obtained from the one of the maximal circle provided one replaces λ with an effective 't Hooft coupling λ = λ cos 2 θ 0 .…”

BPS wilson loops in generic conformal $$ \mathcal{N} $$ = 2 SU(N) SYM theories

“…In both cases it carries a color factor proportional to f abc . This contribution has been proven to vanish long ago [2,15]. The cancellation is justified by symmetry properties of the (finite) integral over the insertion points along the circular loop 6 .…”

“…This computation was extended to finite N in [4] where it was observed that the field-theoretic perturbative expansion of this observable is in fact captured by a Gaussian matrix model. Many extensions and generalizations have been studied in the N = 4 context with either field-theoretic or holographic methods or through relations to integrability [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Wilson loops that preserve a subgroup of the super-conformal symmetry of the N = 4 theory are also instances [21] of a defect conformal field theory [22][23][24] and have been investigated also from this point of view [25][26][27].…”

Antisymmetric Wilson loops in N $$ \mathcal{N} $$ = 4 SYM beyond the planar limit

“…(This is still at the level of conjecture, as the 1-loop fluctuations around the localization locus have not been explicitly evaluated. See [47][48][49] however for several non-trivial checks of the conjecture). Aspects of the matrix model machinery we have employed can be generalized to the study of multi-matrix models.…”