Abstract
We compute a set of correlation functions of operator insertions on the 1/8 BPS Wilson loop in mathcal{N}=4 SYM by employing supersymmetric localization, OPE and the Gram-Schmidt orthogonalization. These correlators exhibit a simple determinant structure, are position-independent and form a topological subsector, but depend nontrivially on the ’t Hooft coupling and the rank of the gauge group. When applied to the 1/2 BPS circular (or straight) Wilson loop, our results provide an infinite family of exact defect CFT data, including the structure constants of protected defect primaries of arbitrary length inserted on the loop. At strong coupling, we show precise agreement with a direct calculation using perturbation theory around the AdS2 string worldsheet. We also explain the connection of our results to the “generalized Bremsstrahlung functions” previously computed from integrability techniques, reproducing the known results in the planar limit as well as obtaining their finite N generalization. Furthermore, we show that the correlators at large N can be recast as simple integrals of products of polynomials (known as Q-functions) that appear in the Quantum Spectral Curve approach. This suggests an interesting interplay between localization, defect CFT and integrability.
Highlights
The exact solution to an interacting quantum field theory in four dimensions would mark a breakthrough in theoretical physics, it still seems out of reach at present time
When applied to the 1/2 BPS circular Wilson loop, our results provide an infinite family of exact defect CFT data, including the structure constants of protected defect primaries of arbitrary length inserted on the loop
We show that the correlators at large N can be recast as simple integrals of products of polynomials that appear in the Quantum Spectral Curve approach
Summary
The exact solution to an interacting quantum field theory in four dimensions would mark a breakthrough in theoretical physics, it still seems out of reach at present time. One can make some progress since there are observables that preserve a fraction of the supersymmetries and are often amenable to exact analytic methods, most notably supersymmetric localization [1]. Another powerful method, which is currently the subject of active exploration, is the conformal bootstrap, see e.g. [2] for a recent review This approach uses conformal symmetry instead of supersymmetry, and has been remarkably successful in deriving bounds on physical quantities in non-trivial CFTs (most notably the 3d Ising model) and in charting a landscape of theories from a minimal set of assumptions [3, 4]. It allows one to compute them exactly as a function of coupling constants, rather than giving general bounds
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