Twisted Boundary Conditions in Lattice Simulations

TL;DR

This paper investigates the use of twisted boundary conditions in lattice QCD simulations, demonstrating their effectiveness in accessing non-integer momenta and analyzing finite-volume effects on various physical quantities.

Contribution

It provides a theoretical study using Chiral Perturbation Theory on finite-volume effects with twisted boundary conditions, including partially twisted cases, and discusses implications for practical lattice simulations.

Findings

Finite-volume effects remain exponentially small with twisted boundary conditions.

Partially twisted boundary conditions do not require new gluon configurations, enhancing practicality.

Twisted boundary conditions break isospin symmetry, affecting decay amplitude determinations.

Abstract

By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2pi/L on a lattice with spatial volume L^3. We use Chiral Perturbation Theory to study finite-volume effects with twisted boundary conditions for quantities without final-state interactions, such as meson masses, decay constants and semileptonic form factors, and confirm that they remain exponentially small with the volume. We show that this is also the case for "partially twisted" boundary conditions, in which (some of) the valence quarks satisfy twisted boundary conditions but the sea quarks satisfy periodic boundary conditions. This observation implies that it is not necessary to generate new gluon configurations for every choice of the twist angle, making the method much more practicable. For K->pipi decays we show that the breaking of isospin symmetry by the twisted boundary conditions implies that the amplitudes cannot be determined in general (on this point we disagree with a recent claim).