Bootstrapping $$ \mathcal{N} $$ = 4 sYM correlators using integrability

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.

“…We found that in order to get a finite result we have to add divergent counter-terms given by insertions of the identity operator. 3 So, in practice we should use…”

Section: From Deformations Of the Mwl To Integrated Correlatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Cavaglià

Gromov

Julius

et al. 2023

“…Following the philosophy of [12][13][14], the results for the spectrum, joined with the constraints from the conformal crossing relations for some correlators could give narrow bounds, or even analytic results for some structure constants. In the current set-up of the local operators our predictions at strong coupling can be fed into the conformal constraints obtained in [53,54].…”

Section: Bootstrabilitymentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Gromov,

Hegedűs,

Julius

et al. 2024

Integrability methods give us access to a number of observables in the planar $$ \mathcal{N} $$ N = 4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum of anomalous dimensions. Low lying states were successfully studied in the past using the QSC. However, with the increased demand for a systematic study of a large number of states for various applications, there is a clear need for a fast QSC solver which can easily access a large number of excited states. Here, we fill this gap by developing a new algorithm and applied it to study all 219 states with the bare dimension ∆0 ≤ 6 in a wide range of couplings.The new algorithm has an improved performance at weak coupling and allows to glue numerics smoothly the available perturbative data, resolving the previous obstruction. Further ∼ 8-fold efficiency gain comes from C++ implementation over the best available Mathematica implementation. We have made the code and the data to be available via a GitHub repository.The method is generalisable for non-local observables as well as for other theories such as deformations of $$ \mathcal{N} $$ N = 4 SYM and ABJM. It may find applications in the separation of variables and bootstrability approaches to the correlation functions. Some applications to correlators at strong coupling are also presented.

“…At the same time, four-point functions are starting points for the conformal bootstrap program [1][2][3]. A better understanding of their analytic properties and perturbative results is important for bootstraping them non-perturbatively [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Giant correlators at quantum level

Jiang,

Wu,

Zhang

2024

We compute four-point functions with two maximal giant gravitons and two chiral primary operators at three-loop order in planar $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory. The Lagrangian insertion method, together with symmetries of the theory fix the integrand up to a few constants. Under the additional assumption of planarity, all these constants can be determined by lower loop data. The obtained result can be regarded as the planar diagram contribution to the full four-point function and is written in terms of the known three-loop conformal integrals. From the four-point function, we extract the OPE coefficients of two giant gravitons and one non-BPS twist-2 operator with arbitrary spin at three-loops, given in terms of harmonic sums. We observe an intriguingly simple relation between the giant graviton OPE coefficients and the OPE coefficients of three single-trace operators.