<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>-insensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:m

The spectrum of two-dimensional adjoint QCD is surprisingly insensitive to the number of colors <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>c</a:mi></a:msub></a:math> of its gauge group. It is argued that the cancellation of finite <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>c</c:mi></c:msub></c:math> terms is rather natural and ultimately a consequence of the singularity structure of the theory. In short, there are no finite <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>c</e:mi></e:msub></e:math> terms, hence effectively there cannot be any finite <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>c</g:mi></g:msub></g:math> singular terms, since the former are necessary to guarantee well-behaved principal value integrals. We evaluate and categorize the matrix elements of the theory’s light-cone Hamiltonian to show how terms emerging from finite <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mi>c</i:mi></i:msub></i:math> contributions to the anticommutator cancel against contributions from the purely finite <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>N</k:mi><k:mi>c</k:mi></k:msub></k:math> term of the Hamiltonian. The cancellation is not complete; finite terms survive and modify the spectrum, as is known from numerical work. Additionally we show that several parton-number changing finite <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>N</m:mi><m:mi>c</m:mi></m:msub></m:math> matrix elements vanish independently of finiteness requirements. In particular, there is only one trace-diagonal finite <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>N</o:mi><o:mi>c</o:mi></o:msub></o:math> correction. It seems therefore that considering matrix elements rather than individual contributions can provide substantial simplifications when computing the spectrum of a theory with a large symmetry group. Published by the American Physical Society 2024