Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1

Abstract

We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT 1 with SU(1, 1|3) superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS 4 × CP 3 ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS 2 Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution.

Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

“…The action of Q + on Q can similarly be read from (D.15), but it misses the descendant. These are fixed instead by requiring closure under the Jacobi identity as in (3.6) (see also for instance the discussion in section 2 of [74]).…”

Superconformal boundaries in 4 − ϵ dimensions

“…In principle one can do explicit perturbative JHEP04(2021)167 calculations as in [43], however it is perhaps simpler to set up a bootstrap problem and attempt to solve it using the technology of inversion formulas [45,46]. One could also concentrate exclusively on three dimensions and apply the numerical bootstrap on the line, analogous to what was done for the twist defect in the 3d Ising model [43] (the 1d bootstrap for superconformal line defects has been studied in [60][61][62]).…”

The topological line of ABJ(M) theory

“…Defect conformal field theories supported on the 1/2 BPS Wilson line have been studied in four-dimensional N = 4 SYM [48,49] and its topological sector has been extensively studied in a series of papers [50][51][52]. The defect conformal field theory related to the 1/2 BPS Wilson line in ABJ(M) theory has been examined in [53], where it has been shown that, at variance with the four-dimensional case, the displacement supermultiplet does not admit a topological sector. Because the relevant symmetry is exactly su(1, 1|3) ⊕ u(1) b we expect that an explicit representation of the topological operators can be constructed, although in terms of supermatrices, as done in [53] for the displacement supermultiplet.…”

“…The defect conformal field theory related to the 1/2 BPS Wilson line in ABJ(M) theory has been examined in [53], where it has been shown that, at variance with the four-dimensional case, the displacement supermultiplet does not admit a topological sector. Because the relevant symmetry is exactly su(1, 1|3) ⊕ u(1) b we expect that an explicit representation of the topological operators can be constructed, although in terms of supermatrices, as done in [53] for the displacement supermultiplet. Work in this direction is in progress [41].…”