Excited states of one-dimensional defect CFTs from the quantum spectral curve

Abstract

We study the anomalous dimension of the cusped Maldacena-Wilson line in planar $$ \mathcal{N} $$ N = 4 Yang-Mills theory with scalar insertions using the Quantum Spectral Curve (QSC) method. In the straight line limit we interpret the excited states of the QSC as insertions of scalar operators coupled to the line. Such insertions were recently intensively studied in the context of the one-dimensional defect CFT. We compute a five-loop perturbative result analytically at weak coupling and the first four orders in the $$ 1/\sqrt{\uplambda} $$ 1 / λ expansion at strong coupling, confirming all previous analytic results. In addition, we find the non- perturbative spectrum numerically and show that it interpolates smoothly between the weak and strong coupling predictions.

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

“…More generally, line defects provide a useful and physically interesting laboratory for the application of the analytical techniques developed in the context of one-dimensional CFTs [13][14][15][16][17][18]. Finite-coupling results on defect conformal data were also obtained using integrability via the quantum spectral curve technology [19].…”

“…A parallel attempt would be to compute the anomalous dimensions of exchanged operators beyond the first non-trivial order using the bootstrap approach: the potential mixing problem discussed above is expected to arise at this level, and its resolution would require the analysis of different correlators. 7 Another very interesting direction could be to apply integrability in this context, as done recently in the N = 4 case [19]. Data at finite coupling for the correlators of interest here may also be obtained with lattice field theory methods applied to the string worldsheet, discretizing the Lagrangian of [41] expanded around the minimal surface corresponding to the 1/2 BPS line, and using Monte Carlo techniques on the lines of [42][43][44][45][46] for the correlators of the worldsheet excitations.…”

“…18 This would just correspond to an overall rescaling of the fields. 19 By evaluating perturbatively the two-point function (5.17) (namely, calcu- 18 This is the formal choice of [5], where the analogue relation is to the N = 4 SYM Bremsstrahlung function [10,82,83]. See also a related discussion in [49].…”

“…See also a related discussion in [49]. 19 Given the leading strong coupling value of the Bremsstrahlung function B 1/2 (λ) = √ 2λ 4π ≡ T 2π , and given our choice (5.19) of the bulk-to-boundary propagator, at tree level this would amount to the rescaling w a → √ 2T w a .…”

“…The first connected contribution to the four-point function comes from the tree-level connected Witten diagrams obtained from the four-point interaction vertices L 4w in (5.15) with four bulk-to-boundary propagators attached, see figure 2, and therefore it is subleading in 1/T . As in [5], we will adopt the normalization [84,85] of the bulk-to-boundary propagator in dimension d = 1 19) for which the tree-level two-point function of the dual boundary operator is…”