Lattice Theories with Nonlinearly Realized Chiral Symmetry

TL;DR

This paper introduces a lattice formulation for effective theories with nonlinearly realized chiral symmetry, enabling non-perturbative studies of baryons, pions, and quark-gluon systems without symmetry-breaking issues.

Contribution

The authors develop a lattice approach that preserves chiral symmetry nonlinearly, allowing for the study of baryon-pion interactions and dense matter without complex action problems.

Findings

Chiral symmetry is preserved in the lattice formulation.

The method enables simulations at non-zero baryon density.

Potential to explore the phase diagram of strongly interacting matter.

Abstract

We present the lattice formulation of effective Lagrangians in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework both the Wilson term removing unphysical doubler fermions and the fermion mass term do not break chiral symmetry. Our lattice formulation allows us to address non-perturbative questions in effective theories of baryons interacting with pions and in models involving constitutent quarks interacting with pions and gluons. With the presented methods, a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering a complex action problem. This might lead to new insights into the phase diagram of strongly interacting matter at non-zero chemical potential.