Correlators of supersymmetric Wilson-loops, protected operators and matrix models in 𝒩 = 4 SYM

Abstract

We study the correlators of a recently discovered family of BPS Wilson loops in N = 4 supersymmetric U (N ) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant g and for any rank N , by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order O(g 4 ) for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at O(g 6 ). This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the N = 4 SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.

Ladder limit for correlators of Wilson loops

“…Exact results for correlators of Wilson loops operators have been obtained before via a matrix model calculations [33,34,35,36,37,38]. Our family of supersymmetric correlators includes the case R 1 = R 2 = R, h = 0 and γ = π, which has been studied with matrix model techniques.…”

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

“…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].…”

Correlators between Wilson loop and chiral operators in $$ \mathcal{N}=2 $$ conformal gauge theories

“…Wilson loops preserving fewer supersymmetries [4], such as the 1/4-BPS circular loop [5] and particular classes of 1/8-BPS loops [6][7][8], have been classified and analyzed. Correlators among such Wilson loops, or between Wilson loops and local operators have also been considered [9][10][11]; in particular, correlators of a 1/8-BPS circular loop and chiral primaries in N = 4 SYM theory have been computed [12][13][14][15][16], mapping them to multi-matrix models. Also correlators with local chiral operators and Wilson loops in higher representations have been discussed [17,18].…”