Confining ensemble of dyons

TL;DR

This work develops a measure for a multi-dyon ensemble in SU($N$) gauge theory at finite temperature by combining the moduli-space metrics of different-kind and same-kind dyons into a hyper-Kähler framework, yielding a 3D quantum field theory with exact boson–ghost cancellations. The resulting vacuum preferentially selects a confining holonomy, giving a zero average Polyakov loop and a linear potential between static quarks with a k-ality dependent string tension that follows a sine law in $N$-ality; the same ensemble also produces an area law for spatial Wilson loops, suggesting Lorentz symmetry restoration in the confining regime. The deconfinement transition and the robust ratio $T_c/ oot2 ext{(σ)}$ align well with lattice data, supporting the idea that the dyon measure plays a decisive role in confinement physics. Although the model omits several YM ingredients, it provides a compelling, solvable framework to connect KvBLL calorons, dyon dynamics, and confinement features through explicit analytic results.

Abstract

We construct the integration measure over the moduli space of an arbitrary number of N kinds of dyons of the pure SU(N) gauge theory at finite temperatures. The ensemble of dyons governed by the measure is mathematically described by a (supersymmetric) quantum field theory that is exactly solvable and is remarkable for a number of striking features: 1) The free energy has the minimum corresponding to the zero average Polyakov line, as expected in the confining phase; 2)The correlation function of two Polyakov lines exhibits a linear potential between static quarks in any N-ality non-zero representation, with a calculable string tension roughly independent of temperature; 3) The average spatial Wilson loop falls off exponentially with its area and the same string tension; 4) At a critical temperature the ensemble of dyons rearranges and de-confines; 5)The estimated ratio of the critical temperature to the square root of the string tension is in excellent agreement with the lattice data.

Figures (1)

• Figure 1: A bunch of profile functions $w_{12}$ (left), $w_{23}$ (middle) and $w_{31}$ (right) inside the $SU(3)$ string for five values of the parameter $\gamma$: ${\rm arg}(\gamma)=(4,5,6,7,8)\times (\pi/9)$. The red solid curves display imaginary parts and the blue dashed curves display real parts of $w_{12},w_{23},w_{31}$, respectively, as functions of the distance $z$ from the Wilson loop plane. The string tension (the action) is identical for all five curves.