Abstract
We discuss Yang-Baxter sigma deformations of 4D Minkowski spacetime proposed recently. To avoid the degeneracy of the standard bilinear form associated with the familiar coset ISO(1,3)/SO(1,3), we consider a slice of AdS5 in Poincaré coordinates by embedding the 4D Poincaré group into the 4D conformal group SO(2,4). With this procedure we present the metrics and B-fields as Yang-Baxter deformations which correspond to well-known backgrounds such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field.
Highlights
Another way is to employ a generalized symmetric two-form [65]
A systematic way is the Yang-Baxter sigma model approach proposed by Klimcik [11,12,13]. It was originally invented for principal chiral models based on the modified classical YangBaxter equation
There are a lot of classical r-matrices satisfying the cybe and some of them are associated with well-known gravitational backgrounds, such as Lunin-Maldacena-Frolov backgrounds [39, 40], gravity duals for non-commutative gauge theories [41, 42], Schrödinger spacetimes [43,44,45,46,47] and gravity duals for dipole theories [48,49,50,51,52], as shown in a series of works [53,54,55,56,57]
Summary
Received: May 22, Revised: September 3, Accepted: October 7, Published: October 28, a Graduate School of Mathematics and Institute for Advanced Research, Nagoya University, Nagoya 464-8602, Japan b
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