Lax pairs on Yang-Baxter deformed backgrounds

Abstract

We explicitly derive Lax pairs for string theories on Yang-Baxter deformed backgrounds, 1) gravity duals for noncommutative gauge theories, 2) $\gamma$-deformations of S${}^5$, 3) Schrödinger spacetimes and 4) abelian twists of the global AdS${}_5$\,. Then we can find out a concise derivation of Lax pairs based on simple replacement rules. Furthermore, each of the above deformations can be reinterpreted as a twisted periodic boundary conditions with the undeformed background by using the rules. As another derivation, the Lax pair for gravity duals for noncommutative gauge theories is reproduced from the one for a $q$-deformed AdS${}_5\times$S${}^5$ by taking a scaling limit.

1+39 pages, v3: typos corrected and the reference [42] added

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Cited by in corpus (1)

• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$