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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.18451 |
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| _version_ | 1866915534333804544 |
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| author | Lindwasser, Lukas W. |
| author_facet | Lindwasser, Lukas W. |
| contents | The Lie algebra of symmetries generated by the left-moving current $j=\partial_-ϕ$ in the $2d$ single scalar conformal field theory is infinite dimensional, exhibiting mutually commuting subalgebras. The infinite dimensional mutually commuting subalgebras define integrable deformations of the $2d$ single scalar conformal field theory which preserve the Poisson bracket structure. We study these mutually commuting subalgebras, finding general properties that the generators of such a subalgebra must satisfy. Along the way, we derive constraints on integrable equations of the Korteweg-de Vries type. We also confirm that the recently found $[j]=0,-1,-2$ mutually commuting subalgebras are infinite dimensional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constraining all possible Korteweg-de Vries type hierarchies Lindwasser, Lukas W. High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems The Lie algebra of symmetries generated by the left-moving current $j=\partial_-ϕ$ in the $2d$ single scalar conformal field theory is infinite dimensional, exhibiting mutually commuting subalgebras. The infinite dimensional mutually commuting subalgebras define integrable deformations of the $2d$ single scalar conformal field theory which preserve the Poisson bracket structure. We study these mutually commuting subalgebras, finding general properties that the generators of such a subalgebra must satisfy. Along the way, we derive constraints on integrable equations of the Korteweg-de Vries type. We also confirm that the recently found $[j]=0,-1,-2$ mutually commuting subalgebras are infinite dimensional. |
| title | Constraining all possible Korteweg-de Vries type hierarchies |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2502.18451 |