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arXiv · 1803.05903

Local $β$-deformations and Yang-Baxter sigma model

Jun-ichi Sakamoto·Yuho Sakatani
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Abstract

Homogeneous Yang-Baxter (YB) deformation of AdS$_5\times$S$^5$ superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to $β$-deformations of the AdS$_5\times$S$^5$ background when the classical $r$-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10,10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing $H$-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study $β$-deformations of $H$-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.

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Jun-ichi Sakamoto, Yuho Sakatani. 2018-07-06. Local $β$-deformations and Yang-Baxter sigma model. https://doi.org/10.1007/jhep06(2018)147

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