Integrated correlators from integrability: Maldacena-Wilson line in $$ \mathcal{N} $$ = 4 SYM

Abstract

We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.

Fast QSC solver: tool for systematic study of $$ \mathcal{N} $$ = 4 Super-Yang-Mills spectrum

“…All of them have Lorentz spin labels (0 0). We present them in table 15. Clearly, all these states are members of the KK-tower [0 0; 0 0], in exact agreement with (6.11), and thus the results of [97].…”

“…Due to this restriction, there are 7 cutP/2 parameters as one of the sets {c a } or {c a } is not independent. 15 The gauge conditions are the most general (4.4) though some one them are trivially satisfied because of parity symmetry. This results in 7 cutP/2 − 1 parameters to start with (cf.…”

“…Yet only a handful of states are available in the literature [1][2][3][4][5][6][7][8][9][10][11]. Recently, new methods became available which utilise a combination of the conformal bootstrap techniques with the insights from integrability to obtain observables beyond the spectrum [12][13][14][15]. The information about the non-perturbative spectrum combined with the conformal bootstrap method is already shown to give very accurate bounds on the structure constants in some examples [12,13].…”

Unmixing the Wilson line defect CFT. Part II. Analytic bootstrap

“…It is also worth mentioning that the same model considered here has recently been subject of thorough investigations using a combination of integrability and numerical bootstrap methods, a technique that has been dubbed "bootstrability" [12][13][14]131]. This exploits the knowledge of the spectrum from integrability as an input for a numerical bootstrap algorithm, which combined with the integrated correlator constraints found in [14,131,132] has been shown to put stringent bounds on the OPE coefficients of certain long multiplets. All of these developments make the half-BPS Wilson line defect an extremely interesting playground where one can learn how to combine different approaches in an attempt to completely solve the model.…”

“…This is true in particular for higher-point functions, which have only recently become subject of investigations in the context of the analytic bootstrap [61,62,[133][134][135][136]. 51 Moreover, the integrated correlator constraints of [14,131,132] have not played a role in our analysis, 52 but could be instrumental to the study of these 51 See also [120] for a recent computation of a six-point function on the half-BPS Wilson line in N = 4 SYM from direct computation using a novel method. 52 One can check, however, that they are satisfied, which provides a further consistency check of the validity of our results.…”