Chiral Lagrangians from lattice gauge theories in the strong coupling limit

TL;DR

This paper derives chiral Lagrangians from lattice gauge theories using the large-N limit and color-flavor transformation, demonstrating spontaneous chiral symmetry breaking patterns without assumptions.

Contribution

It provides a rigorous derivation of nonlinear sigma models for various symmetric spaces directly from lattice gauge theories in the strong coupling limit.

Findings

Proves spatial homogeneity of meson vacuum configurations.

Establishes spontaneous chiral symmetry breaking patterns.

Uses Zirnbauer's color-flavor transformation for derivation.

Abstract

We derive nonlinear sigma models (chiral Lagrangians) over symmetric spaces U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge theories coupled to n flavors of staggered fermions, in the large-N and g^2 N limit. To this end, we employ Zirnbauer's color-flavor transformation. We prove the spatial homogeneity of the vacuum configurations of mesons by explicitly solving the large-N saddle point equations, and thus establish the above patterns of spontaneous chiral symmetry breaking without any assumptions.