Structure constants of operators on the Wilson loop from integrability

Abstract

Abstract:We study structure constants of local operators inserted on the Wilson loop in N = 4 super Yang-Mills theory. We conjecture the finite coupling expression of the structure constant which is interpreted as one hexagon with three mirror edges contracted by the boundary states. This is consistent with a holographic description of the correlator as the cubic open string vertex which consists of one hexagonal patch and three boundaries. We check its validity at the weak coupling where the asymptotic expression reduces to the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factor. For this purpose, we compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The result is nicely matched with our conjecture at the weak coupling regime.

Correlation functions on the Half-BPS Wilson loop: perturbation and hexagonalization

“…Based on this observation, in section 5 we present a refined version of the conjecture on the hexagon formalism for the non-BPS structure constants on the 1/2-BPS Wilson loop, which was given originally in [43]. Finally in section 6, we conclude and comment on future directions.…”

“…The idea of computing the three-point functions on the Wilson loop from hexagons was proposed originally in [43]. However, our analysis suggests the necessity of the refinement of the proposal [43], which we will describe shortly.…”

“…Through the comparison, we conjecture that the three-point function on the Wilson loop can be decomposed into one hexagon and three boundary states (see figure 2), where the relevant boundary state was determined in the study of the spectrum on the Wilson loop [40,41]. The idea of computing the three-point functions on the Wilson loop from hexagons was proposed originally in [43]. However, our analysis suggests the necessity of the refinement of the proposal [43], which we will describe shortly.…”

Non-supersymmetric Wilson loop in $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT

“…At the same time, the 3-point scalar Φ 6 correlator at the ζ = 1 point is non-trivial (cf. also [36,37]). In general, on the 1/2-BPS circular WL we should have…”

Cutting the cylinder into squares: the square form factor

“…It is worth pointing that a different square form factor from the one proposed here has appeared in the context of correlation functions of three separated operators connected by Wilson lines [31]. Despite the different nature of both squares, we expect them to fulfil similar consistency conditions.…”