Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations

Abstract

The two-and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the 3PI effective action. Within a self-contained truncation various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.

Nonperturbative finite-temperature Yang-Mills theory

“…At high temperatures, this zero crossing moves then to higher scales, which is in line with the high temperature limit and [72]. This qualitative argument is actually independent of the type of the solution, since the threedimensional ghost triangle diagram diverges with a powerlaw in the case of the scaling solution and linearly [6,49,51] in the case of the decoupling solution. We find that the zero crossing of the electric component vanishes at a temperature of T ≈ 40 MeV.…”

“…At zero temperature, the three-gluon vertex shows a zero crossing in four as well as in three dimensions [2,6,46,49,[51][52][53]59,[132][133][134][135]. Analytical studies show that it is caused by the divergent ghost triangle diagram.…”

“…While lattice simulations struggle with the sign problem, functional methods have to address the resonant interaction structure, which requires particularly advanced truncations of the corresponding generating functionals. The tremendous progress in functional approaches to QCD has recently led to a shift from qualitative bottom-up towards quantitative top-down approaches [1][2][3][4][5][6]; see also [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] for reviews. In particular, the functional renormalisation group (FRG) is a first-principles method that allows for quantitative computations of the generating functional of QCD.…”

Baryons as relativistic three-quark bound states

“…To systemetise this procedure until apparent convergence is reached is at the heart of modern treatments of the tower of DSEs, see e.g. [205][206][207][208][209][210] and references therein. Other strategies are possible and are discussed below and in the course of this review.…”

A stochastic root finding approach: the homotopy analysis method applied to Dyson–Schwinger equations

“…We could go up to correlation length 5 for the 2D model where further increase is limited by the sign problem. In future work, the following two major questions must be addressed: the first one is about the quality of the truncation of the DSEs, which has partly already been addressed in previous works on DSEs [46][47][48] and within the functional renormalization group community [37,38,49]. It has been shown that truncating the average effective action in the fRG approach by using a low order derivative and field expansion yields already good results for the critical exponents of 4 f models [37].…”