Sign problems, noise, and chiral symmetry breaking in a QCD-like theory

• Published in: arXiv.org
• Main Authors: Grabowska, Dorota, Kaplan, David B, Nicholson, Amy N
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 24.01.2013
• Subjects: Broken symmetry; Chemical potential; Correlation analysis; Fermions; Flavor (particle physics); Formulations; Mathematical models; Organic chemistry; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Theory
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1208.5760

The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path integral formulations: at finite chemical potential one formulation has a severe sign problem similar to that found in QCD, while the other does not. At large N, where N is the number of flavors, one can compute the probability distributions of fermion correlators analytically in both formulations. In the former case one finds a broad distribution with small mean; in the latter one finds a heavy tailed positive distribution amenable to the cumulant expansion techniques developed in earlier work. We speculate on the implications of this model for QCD.