Kenneth Wilson and Lattice QCD

Abstract

We discuss the physics and computation of lattice QCD, a spacetime 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.

From hadrons to quarks in neutron stars: a review

“…Owing to the inability of lattice gauge theory calculations to describe cold matter at finite baryon density, due the fermion sign problem [81], one needs to adopt phenomenological models of interacting quarks in order to describe dense quark matter in neutron star cores [47,108,109,[144][145][146][147]. We discuss here the frequently employed Nambu-Jona-Lasinio (NJL) model [139,141,142], which replaces the full QCD interactions with effective quark-quark interactions, while at the same time suppressing explicit gluonic degrees of freedom.…”

Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

“…Not only did Wilson offer an explanation why no free quarks appear in Nature, he also introduced his so-called Wilsonian path integral which enables to numerically compute expectation values using the Monte-Carlo method [2]. With the increasing computing power, this method has since its first results at the end of the Seventies [3] produced by far the most impressive results for QCD [4,5]. Examples include the determination of the light hadron masses [6], the determination of the quark masses [7] and obtaining the phase diagram at finite temperature [8].…”

Construction of a model of monopolium and its search via multiphoton channels at LHC

“…The bound state of the monopoles is formed by the exchange of magnetic photons γ M . However, the coupling of the monopole to the magnetic photon is very strong, so that we adopt a lattice gauge theory approach with a lattice constant a as a UV cutoff [11,12,13]. The space-time is considered to be a square lattice n = (n 0 , n 1 , n 2 , n 3 ) (n µ is an integer) with a lattice constant a.…”

“…In the action, we assume that the magnetic coupling g is strong and , while the electric coupling e is weak and perturbative. So, in estimating the expectation value of the large Wilson loop W (B) [C], the strong coupling expansion is used [11,12,13]. We choose C to be a rectangle of length T in time and length r in the space-like direction ν; then we have…”

“…The difficulty of highly charged particles is the estimation of the potential between them. One photon exchange is not enough, and so we will use lattice gauge theory with a finite lattice constant a, in which a strong coupling expansion is possible [11,12,13]. We will apply this to the magnetic U(1) part of the manifestly electromagnetic dual formulation of Zwanziger [14,15].…”