Calculating the chiral condensate of QCD at infinite coupling using a generalised lattice diagrammatic approach

TL;DR

This paper introduces a new lattice diagrammatic method to calculate the QCD chiral condensate at infinite coupling, involving resummation of gauge link diagrams and a novel group integral evaluation technique, revealing non-zero solutions for all Nf.

Contribution

The paper presents a generalized diagrammatic approach with a new group integral technique to compute the chiral condensate, extending previous methods to include multiple diagram types and analyze convergence.

Findings

Calculated chiral condensate as a function of Nf

Found two non-zero solutions for all integer Nf

Observed signs of convergence at small Nf

Abstract

We develop a lattice diagrammatic technique for calculating the chiral condensate of QCD at infinite coupling inspired by recent work of Tomboulis and earlier work from the 80's. The technique involves calculating the contribution of gauge link diagrams formed from all possible combinations of a number of sub-diagram types. This is achieved by performing a resummation, using a truncated number of sub-diagram types. We show how to calculate the relevant sub-diagrams, including a new technique for evaluating group integrals with arbitrary number of gauge link elements, using Young Projectors. Including up to four different diagram types we calculate the chiral condensate as a function of Nf, and show that two real solutions result, which are non-zero for all integer Nf. We analyse these solutions and find signs of convergence of the expansion at small Nf. We discuss sources of error associated with this approach in detail and implement a technique to reduce over-counting of diagrams.