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arXiv · 2502.18451

Constraining all possible Korteweg-de Vries type hierarchies

Lukas W. Lindwasser
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Abstract

The Lie algebra of symmetries generated by the left-moving current $j=\partial_-\phi$ 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.

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Lukas W. Lindwasser. 2025-02-25. Constraining all possible Korteweg-de Vries type hierarchies. https://doi.org/10.1103/lsp2-p3b2

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