Abstract
We build string backgrounds for Yang-Baxter deformations of the AdS4 × ℂℙ3 superstring generated by r-matrices satisfying the classical Yang-Baxter equation. We obtain the metric and the NSNS two-form of the gravity dual corresponding to noncommutative and dipole deformations of ABJM theory, as well as a deformed background with Schrödinger symmetry. The first two backgrounds may also be found by TsT transformations while for the last background we get a new family of non-relativistic ABJM theories with Schrödinger symmetry.
Highlights
It is possible to consider r-matrices that are solutions of the classical Yang-Baxter equation (CYBE)
The first two backgrounds may be found by TsT transformations while for the last background we get a new family of non-relativistic ABJM theories with Schrödinger symmetry
In these cases the r-matrices are all Abelian. These results were extended to the nonabelian case [31] and it was conjectured [32] that deformations using solutions of the CYBE are equivalent to nonabelian T-duality transformations [33, 34]
Summary
The action for the Yang-Baxter σ-model on a Lie superalgebra g of a supergroup G with Z4 grading is given by [8]. The operator d and its transpose d are 2 d = P1 + 1 − cη P2 − P3,. Where Pi (i = 1, 2, 3) are the projectors on each subalgebra of g except P0 on g(0) This is required in order to have a g(0)-invariant action. R is the operator associated to the Yang-Baxter equation (YBE) which can be written, in its modified version, as c=0 [RM, RN ] − R ([RM, N ] + [M, RN ]) = c [M, N ] , c = ±1. In (2.1) and (2.8) the parameter c refers to either the classical YangBaxter (CYBE) equation or to the modified classical Yang-Baxter equation (mCYBE)
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