S-duality invariant perturbation theory improved by holography

TL;DR

This paper develops S-duality invariant interpolating functions to approximate operator dimensions in $ ext{SU}(N)$ $ ext{N}=4$ SYM, integrating perturbative, holographic, and bootstrap results, revealing insights into the conformal manifold and operator spectrum.

Contribution

It introduces a novel class of interpolating functions that unify perturbative, holographic, and S-duality constraints for operator dimensions in $ ext{N}=4$ SYM.

Findings

Interpolating functions peak at the duality-invariant point $ au = e^{i heta}$.

The conformal manifold maps almost onto a line in the space of operator dimensions.

Interpolating functions for the Konishi operator agree well with TBA numerical results.

Abstract

We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling $\tau$. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the $\mathcal{N}=4$ superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points $\tau =i$ and $\tau =e^{i\pi /3}$. It turns out that our interpolating functions have maximum at $\tau =e^{i\pi /3}$, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.