On Yang-Baxter models, twist operators, and boundary conditions

Abstract

We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations. We also use twist operators to rederive the well-known interpretation of TsT transformations -- equivalent to abelian deformations -- in terms of twisted boundary conditions. We discuss complications in extending this boundary condition picture to non-abelian deformations.

v3, 15 pages, corrected typo in equation (2.4), otherwise matches v2 and published version

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• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
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Cited by in corpus (10)

• $T\bar{T}$ deformations as TsT transformations
• Unimodular jordanian deformations of integrable superstrings
• Dressing cosets and multi-parametric integrable deformations
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• Yang-Baxter deformations of the flat space string
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$