Two-point sum-rules in three-dimensional Yang-Mills theory

TL;DR

This paper calculates the stress-tensor two-point function in three-dimensional Yang-Mills theory at three loops, testing glueball mass estimates from sum rules against lattice data and exploring applications to higher-spin operators.

Contribution

It provides the first three-loop perturbative calculation of the stress-tensor two-point function in 3D Yang-Mills and applies sum-rule techniques to estimate glueball properties.

Findings

Stable estimates for the lightest glueball mass consistent with lattice results.

Estimated glueball coupling to the stress tensor.

Discussion on the non-rigorous nature of sum-rule estimates.

Abstract

We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.