Chiral Perturbation Theory on the Lattice; Strong Coupling Expansion

TL;DR

This paper calculates the coefficients of the effective chiral Lagrangian to order p^4 using strong coupling and large-N expansion on a hypercubical lattice, providing a foundation for numerical methods beyond strong coupling.

Contribution

It explicitly performs the functional integral over fundamental degrees of freedom to derive the effective chiral Lagrangian on a lattice preserving Euclidean invariance.

Findings

Derived coefficients of the chiral Lagrangian to O(p^4)

Performed calculations on a Body Centered Hypercubical lattice

Discussed numerical approaches outside the strong-coupling regime

Abstract

We evaluate the coefficients of the effective chiral Lagrangian to $O(p^4)$ in the strong coupling, large-N expansion. In this limit we explicitly perform the functional integral over fundamental degrees of freedom and obtain the effective chiral Lagrangian. We perform this calculation on the Body Centered Hypercubical lattice which preserves Euclidean invariance to order $p^4$. We further discuss how the coefficients could be obtained numerically, out of the strong-coupling domain.