Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED

Understand

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields.

• For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$ symmetry.
• By adding a four-fermion term we can break the U_A(1) symmetry and thus incorporate the physics of the QCD anomaly.
• We can also tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles.