PIRSA:13120068 Scientific Series Quantum Fields and Strings

DOI10.48660/13120068

Series: Quantum Fields and Strings

Cortes Cubero, A. (2013). Integrability (and Near Integrability) in Matrix-valued Field Theories. Perimeter Institute. https://pirsa.org/13120068

Cortes Cubero, Axel. Integrability (and Near Integrability) in Matrix-valued Field Theories. Perimeter Institute, Dec. 13, 2013, https://pirsa.org/13120068 

@misc{ pirsa_PIRSA:13120068,
  doi = {10.48660/13120068},
  url = {https://pirsa.org/13120068},
  author = {Cortes Cubero, Axel},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Integrability (and Near Integrability) in Matrix-valued Field Theories},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {dec},
  note = {PIRSA:13120068 see, \url{https://pirsa.org}}
}

Abstract

The principal chiral sigma model (PCSM) in 1+1 dimensions is asymptotically free and has as SU(N)-valued field with massive excitations. We have found all the exact form factors and two-point function of the Noether-current operators at large N using the integrable bootstrap program. At finite N, only the first non-trivial form factors are found, which give a good long distance approximation for the two-point function. We show how to use these new exact results to study non-integrable deformations. One example is the PCSM coupled to a Yang-Mills field. One can approximate the spectrum of the meson-like bound states using our form factors. We also examine an anisotropic version of (2+1)-dimensional Yang-Mills theory, which can be interpreted as an array of coupled PCSM’s.

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