Lax pairs for deformed Minkowski spacetimes

Abstract

We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical $r$-matrices with Poincaé generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.

29 pages

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Cited by in corpus (7)

• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Deformations of the Almheiri-Polchinski model
• Sigma models with local couplings: a new integrability -- RG flow connection
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Killing spinors from classical r-matrices
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background