Lattice QCD with a chiral twist

TL;DR

This paper discusses twisted mass QCD, a lattice regularisation method that leverages chiral symmetry to improve computational properties, while addressing symmetry breaking and finite-volume formulations.

Contribution

It introduces twisted mass QCD as a lattice regularisation inspired by continuum chiral symmetry, highlighting its advantages and symmetry-breaking aspects, and explores finite-volume Schrödinger functional applications.

Findings

Twisted mass QCD avoids unphysical zero modes.

It enables automatic O(a) improvement.

Applications to renormalization in finite-volume QCD.

Abstract

In these lectures I explain how chiral symmetry of continuum QCD naturally leads to a class of lattice regularisations known as twisted mass QCD (tmQCD). As compared to standard Wilson quarks, its advantages are the absence of unphysical zero modes, the possibility to circumvent lattice renormalisation problems and automatic O(a) improvement. On the other hand, the physical parity and flavour symmetries are explicitly broken. I discuss these aspects and then turn to the theory in a finite space-time volume with Schroedinger functional boundary conditions. Again, chiral transformations of the continuum theory may be used as a guide to formulate an alternative lattice regularisation of the Schr\"odinger functional, with interesting applications to renormalization problems in QCD.