Large- N Principal Chiral Model in Arbitrary External Fields

We report the explicit solution for the vacuum state of the two-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>SU</a:mi></a:mrow><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> principal chiral model at large <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>N</e:mi></e:mrow></e:math> for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free quantum field theory. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>SU</g:mi></g:mrow><g:mo stretchy="false">(</g:mo><g:mi>N</g:mi><g:mo stretchy="false">)</g:mo></g:math> Dynkin diagram. Published by the American Physical Society 2024