Exact Results for the SU(∞) Principal Chiral Model

22nd International Conference on Integrable Systems and Quantum Symmetries

Orland, Peter^1,2

Baruch College, City University of New York, 17 Lexington Avenue, New York

NY

10010, United States^1

Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York

NY

10016, United States^2

关键词: 1/N-expansion;    Correlation function;    Exact results;    Field theory;    Form factors;    Perturbation theory;    Quantized fields;    Sigma model;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/563/1/012022/pdf
DOI  :  10.1088/1742-6596/563/1/012022

来源: IOP

【 摘 要 】

Exact correlation functions of N × N matrix-valued quantized fields are not generally known, even as N approaches infinity (the planar limit). This is in stark contrast to isovector field theories, which have straightforward 1/N-expansions. I review the method by which exact correlation functions of the large-N limit (1 + 1)-dimensional sigma model with SU(N) × SU(N) symmetry. This field theory is asymptotically free, with a dynamically generated mass gap. The technique is a combination of the 1/N-expansion of the S matrix and Smirnov's form-factor axioms. I briefly discuss how to extract the short-distance behavior of the exact correlation function, which can be compared with perturbation theory.