Abstract
We consider the finite-volume spectra of QCD in the chiral limit of massless up and down quarks and massive strange quarks in the baryon number sectors $B = 0$ and $B = 1$ for different values of the isospin. Spontaneous symmetry breaking gives rise to rotor spectra, as the chiral order parameter precesses through the vacuum manifold. Baryons of different isospin influence the motion of the order parameter through non-trivial Berry phases and associated abstract monopole fields. Our investigation provides detailed insights into the dynamics of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new light on Berry phases in the context of quantum field theory. Interestingly, the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons equation of motion on the vacuum manifold $SU(2) = S^3$.
Highlights
Nowadays lattice QCD calculations are performed close to the physical point, i.e., with realistic quark masses
We focus our theoretical study on this somewhat academic limit in order to gain a deeper understanding of the dynamics of spontaneous chiral symmetry breaking in a finite volume
It should be noted that the nucleon mass, which originates from spontaneous chiral symmetry breaking, remains nonzero in the chiral limit in a finite volume
Summary
Nowadays lattice QCD calculations are performed close to the physical point, i.e., with realistic quark masses. It should be noted that the nucleon mass, which originates from spontaneous chiral symmetry breaking, remains nonzero in the chiral limit in a finite volume This is the case even when all vacuum states are sampled by the precessing order parameter, such that, at least in a naive sense, chiral symmetry is no longer spontaneously broken. While the analog of the Goldstone pions in QCD are massless spinwaves (or magnons) in an antiferromagnet, the condensed matter analog of protons and neutrons are holes or electrons doped into an antiferromagnet In this case, again Berry phases and corresponding monopole fields describe how a doped hole or electron influences the rotor spectrum associated with the precessing staggered magnetization [2].
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