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Constraining all possible Korteweg–de Vries type hierarchies

Lukas W. Lindwasser*

  • *Contact author: llindwasser@ntu.edu.tw
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Phys. Rev. D 112, 085004 – Published 6 October, 2025

DOI: https://doi.org/10.1103/lsp2-p3b2

Abstract

The Lie algebra of symmetries generated by the left-moving current j=∂−ϕ in the two-dimensional (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 that 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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Phys. Rev. D 112, 085004– Published 6 October, 2025
  • Received 30 June 2025
  • Accepted 12 September 2025
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