Kenneth Wilson and lattice QCD

TL;DR

This paper reviews the development and achievements of lattice QCD, highlighting its role in understanding strong interactions, quark confinement, and related phenomena through advanced algorithms and supercomputing.

Contribution

It provides a comprehensive overview of lattice QCD's conceptual foundations, computational challenges, algorithmic innovations, and significant physics results, emphasizing Kenneth Wilson's foundational role.

Findings

Understanding of quark confinement and hadron spectrum

Determination of CKM matrix elements and CP violation

Insights into quark-gluon plasma at high temperatures

Abstract

We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.