Resummation and S-duality in N=4 SYM

TL;DR

This paper develops S-duality consistent resummation methods for anomalous dimensions in N=4 SYM, providing predictions across the coupling space and confirming compatibility with bootstrap bounds and duality invariance.

Contribution

It introduces new resummation prescriptions respecting S-duality, enabling predictions of anomalous dimensions at all coupling values in N=4 SYM.

Findings

Predictions align with conformal bootstrap bounds.

Anomalous dimensions at duality-invariant points match conjectures.

Dimensions vary narrowly around a straight line across the moduli space.

Abstract

We consider the problem of resumming the perturbative expansions for anomalous dimensions of low twist, non-BPS operators in four dimensional N=4 supersymmetric Yang-Mills theories. The requirement of S-duality invariance imposes considerable restrictions on any such resummation. We introduce several prescriptions that produce interpolating functions on the upper half plane that are compatible with a subgroup of the full duality group. These lead to predictions for the anomalous dimensions at all points in the fundamental domain of the complex gauge coupling, and in particular at the duality-invariant values \tau=i and \tau=exp(i\pi/3). For low-rank gauge groups, the predictions are compatible with the bounds derived by conformal bootstrap methods for these anomalous dimensions; within numerical errors, they are in good agreement with the conjecture that said bounds are saturated at a duality-invariant point. We also find that the anomalous dimensions of the lowest twist operators lie within an extremely narrow window around a straight line as we vary the moduli of the theory over the two dimensional fundamental domain.