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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2405.02489 |
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| _version_ | 1866929363267616768 |
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| author | Trittmann, Uwe |
| author_facet | Trittmann, Uwe |
| contents | The spectrum of two-dimensional adjoint QCD is surprisingly insensitive to the number of colors $N_c$ of its gauge group. It is argued that the cancellation of finite $N_c$ terms is rather natural and a consequence of the singularity structure of the theory. In short, there are no finite $N_c$ contraction terms, hence there cannot be any finite $N_c$ 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 $N_c$ contributions to the anti-commutator cancel against contributions from the purely finite $N_c$ 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 $N_c$ matrix elements vanish. In particular, there is only one trace-diagonal finite $N_c$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $N_c$-insensitivity of QCD$_{2A}$ Trittmann, Uwe High Energy Physics - Theory The spectrum of two-dimensional adjoint QCD is surprisingly insensitive to the number of colors $N_c$ of its gauge group. It is argued that the cancellation of finite $N_c$ terms is rather natural and a consequence of the singularity structure of the theory. In short, there are no finite $N_c$ contraction terms, hence there cannot be any finite $N_c$ 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 $N_c$ contributions to the anti-commutator cancel against contributions from the purely finite $N_c$ 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 $N_c$ matrix elements vanish. In particular, there is only one trace-diagonal finite $N_c$ 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. |
| title | On the $N_c$-insensitivity of QCD$_{2A}$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.02489 |