The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension

TL;DR

This paper develops a systematic expansion scheme within the Hamiltonian approach to 2+1 dimensional Yang-Mills theory, refining the calculation of the vacuum wave function and string tension, and showing small corrections that align well with lattice results.

Contribution

It introduces a recursive solution to the Schrödinger equation and re-expresses correlator computations in a two-dimensional chiral boson framework, providing refined string tension estimates.

Findings

Corrections to string tension are between -0.3% and -2.8%.

The approach aligns theoretical predictions more closely with lattice data.

The method offers a systematic way to improve Yang-Mills calculations.

Abstract

We carry out further analysis of the Hamiltonian approach to Yang-Mills theory in 2+1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schrodinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range -0.3% to -2.8%, moving our prediction closer to the recent lattice estimates.