Quarks with Twisted Boundary Conditions in the Epsilon Regime

Abstract

We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the $SU(2{)}_L\times SU(2{)}_R$ chiral theory with non-degenerate quarks and the $SU(3{)}_L\times SU(3{)}_R$ chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.

15 pages, 4 figures

References in corpus (4)

• Twisted Boundary Conditions in Lattice Simulations
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Twisted valence quarks and hadron interactions on the lattice
• Flavor Twisted Boundary Conditions and the Nucleon Axial Current

Cited by in corpus (20)

• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Finite volume corrections to pi-pi scattering
• A New Method for Determining $F_{\pi }$ on the Lattice
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Flavor Twisted Boundary Conditions and the Nucleon Vector Current
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Exponential reduction of finite volume effects with twisted boundary conditions
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Determining F_pi from spectral sum rules
• Probing the chiral weak Hamiltonian at finite volumes
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Low-Energy QCD in the Delta Regime
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Multiparticle tunneling in diffusive superconducting junctions
• Lattice QCD with fixed topology
• The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant
• Extracting the electro-magnetic pion form factor from QCD in a finite volume