Abstract
We consider a Jordanian deformation of the AdS_5xS^5 superstring action by taking a simple R-operator which satisfies the classical Yang-Baxter equation. The metric and NS-NS two-form are explicitly derived with a coordinate system. Only the AdS part is deformed and the resulting geometry contains the 3D Schrodinger spacetime as a subspace. Then we present the full solution in type IIB supergravity by determining the other field components. In particular, the dilaton is constant and a R-R three-form field strength is turned on. The symmetry of the solution is [SL(2,R)xU(1)^2] x [SU(3)xU(1)] and contains an anisotropic scale symmetry.
Highlights
The task is to consider integrable deformations
In the previous work [43], we have considered Jordanian deformations of the AdS5×S5 superstring action by using linear R-operators satisfying the classical Yang-Baxter equation (CYBE), rather than modified classical Yang-Baxter equation (mCYBE)
The symmetry of the solution is given by SL(2, R) × U(1)2 × [SU(3) × U(1)] and contains an anisotropic scale symmetry
Summary
Let us consider an explicit example of Jordanian deformations by taking a skew-symmetric classical r-matrix,. The r-matrix (2.13) induces the action of the associated R-operator as RJor(E22). This mapping rule is obtained from the relation (2.11). Note that the r-matrix (2.13) does not preserve the real-form condition of su(2, 2|4) It leads to a real string action, as we will see later. In order to determine the string background completely, it is still necessary to fix the other field components by solving the field equations of motion in type IIB supergravity. The present example may be regarded as Jordanian twists [36,37,38], though this fact is not manifest from the expression of the r-matrix (2.13)
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