Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve

Abstract

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the 't Hooft coupling λ are sent to infinity with the ratio J/ √ λ fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green's functions on the worldsheet. We derive a representation of the Green's functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green's functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

“…They define a set of correlators respecting the properties of a 1D CFT [31]. These physical observables have been investigated intensively in the past few years with a wide variety of methods, from string and gauge theory computations to localisation, integrability and the conformal bootstrap [17,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] (for less supersymmetric setups see e.g. [45][46][47]).…”

“…There has been progress in this direction [16,20] (for other limits see e.g. [14,38,44]) but a full solution is still missing. Having non-perturbative data obtained with the help of bootstrap methods could be important to inform these efforts.…”

The SAGEX review on scattering amplitudes Chapter 8: Half BPS correlators

“…A number of theories with non maximal supersymmetry whose half BPS correlators exhibit higher dimensional conformal symmetry (which does not seem to be present for the 3d N = 8 or the 6d (2, 0) theories) have been investigated recently in 1d (dual to theories on AdS 2 × S 2 ) [116] and 2d (dual to theories on AdS 3 × S 3 ) [218][219][220][221] as well as theories dual to AdS 5 × S 3 [222,223]. Also of recent interest has been the theories which live inside defects in QFT, and in this context many results for half BPS operators in the 1d theory living on a Wilson line within N = 4 SYM have been found [224][225][226][227][228][229][230][231][232][233][234][235][236].…”

Bootstrability in defect CFT: integrated correlators and sharper bounds

“…There has been progress in this direction [16,20] (for other limits see e.g. [14,38,44]) but a full solution is still missing. Having non-perturbative data obtained with the help of bootstrap methods could be important to inform these efforts.…”

“…They define a set of correlators respecting the properties of a 1D CFT [31]. These physical observables have been investigated intensively in the past few years with a wide variety of methods, from string and gauge theory computations to localisation, integrability and the conformal bootstrap [17,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] (for less supersymmetric setups see e.g. [45][46][47]).…”