Bootstrapping $$ \mathcal{N} $$ = 4 super-Yang-Mills on the conformal manifold

Abstract

We combine supersymmetric localization results with numerical bootstrap techniques to compute upper bounds on the low-lying CFT data of $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory as a function of the complexified gauge coupling τ. In particular, from the stress tensor multiplet four-point function, we extract the scaling dimension of the lowest-lying unprotected scalar operator and its OPE coefficient. While our method can be applied in principle to any gauge group G, we focus on G = SU(2) and SU(3) for simplicity. At weak coupling, the upper bounds we find are very close to the corresponding four-loop results. We also give preliminary evidence that these upper bounds become small islands under reasonable assumptions.

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

“…Later in [35], the same algorithm was used to produce data for higher spin operators J = 2, 4, 6, for a large range of coupling values g ∈ [0. 1,8]. In figure 3 we show data provided by the ancillary of [35].…”

“…As in the g = 0.1 case, the optimal functional does not exhibit zeros near the subleading trajectory, but it exhibits zeros on several operators on the leading trajectory. 8 This is plotted in figure 13, along with the contributions from some individual functionals.…”

“…This boundary data was instrumental in recent perturbative scattering amplitudes and form factors which reached a record high loop order (8 loops) [4] and high multiplicity (up to seven-points) [5,6]. In the strong coupling limit, most efforts have focused on correlators of 1 2 -BPS operators, which is primarily driven by string theory, supergravity, conformal bootstrap, and supersymmetric localization [7,8] techniques. Stringy corrections [9][10][11] and non-planar corrections [12,13] have been computed for four points, while the highest multiplicity correlator is the tree-level five-point function [14], obtained by exploiting all existing constraints.…”

“…The latter combines unitarity, crossing symmetry, and other nonperturbative constraints to resolve the spectrum of a generic conformal field theory and to bound its OPE coefficients; see [28] for a recent review of numerical bootstrap results. In the context of N = 4 sYM, this method provides a handle into energy-momentum correlation functions for finite gauge groups SU(N c ) [29], and, when combined with exact results from localization, arbitrary 't Hooft coupling [8].…”

Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite ε

“…Here the level repulsion between Konishi and the first double-trace operator would be observable in a study at large but finite N c , and at finite coupling. With the recent localization techniques for inserting the value of the coupling constant into the bootstrap system [87], this problem looks tractable.…”