Abstract
We study at perturbative level the correlation functions of a general class of 1/8 BPS Wilson loops and chiral primaries in N = 4 Super Yang-Mills theory. The contours and the location of operator insertions share a sphere S^2 embedded into spacetime and the system preserves at least two supercharges. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer.
Highlights
We study at perturbative level the correlation functions of a general class of 1/8 BPS Wilson loops and chiral primaries in N = 4 Super Yang-Mills theory
This procedure in turn generalizes to a large class of N = 2 theories, where Wilson loops can be accurately studied [9,10,11] through matrix model techniques
In the case of N = 4, the 1/2-BPS circle can be generalized to Wilson loops of arbitrary shapes with lower degree of supersymmetry [12]
Summary
The Wilson loops that we consider in this paper are generically 1/8-BPS operators and have been constructed in [12]. We consider a second configuration, where the operator is inserted at an arbitrary point and the loop is wrapped at the equator: here, as we will see, interactions are expected to contribute non-trivially to the final result. In both cases we consider the large N limit, in which just planar contributions are taken into account. We begin by considering the correlation function between a Wilson loop lying on a latitude of S2 and a chiral primary operator inserted at the north pole. This choice will simplify our analysis and at two-loop level does not represent a real limitation: no new class of perturbative diagrams would enter the computation and the general case should be tamed by simple combinatorics
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