Abstract
The gravity dual of β-deformed ABJM theory can be obtained by a TsT transformation of AdS4 × ℂℙ3. We present a supercoset construction of ℂℙ3 to obtain this gravity dual theory as a Yang-Baxter deformation. This is done by selecting a convenient combination of Cartan generators in order to get an Abelian r-matrix satisfying the classical Yang-Baxter equation. Our results provide another illustration of the relation between Abelian r-matrices and TsT transformations.
Highlights
JHEP11(2018)043 the classical Yang-Baxter equation (CYBE) [15]
Another well known gauge/gravity duality is for the AdS4/CF T3 case which establishes a correspondence between Type IIA superstring theory in AdS4 × CP3 and N = 6 superconformal Chern-Simons-matter theory [30]
All of the analysis that lead to the formulation of Yang-Baxter deformations in AdS5 × S5 can in principle be extended to AdS4 × CP3
Summary
There are only two superstring sigma models with vanishing β-function in ten dimensional semi-symmetric spaces, AdS5 × S5 and AdS4 × CP3 [34]. Type IIA superstrings moving in AdS4 ×CP3 can be described by a sigma model formulated in the coset (1.1). The coset description of AdS4 × CP3 is missing 8 fermions and, lacks the correct amount of supersymmetry of usual GS superstrings. We can go around this problem arguing that the 8 missing fermions are part of the 16 fermionic degrees of freedom that are removed by κsymmetry. In this way the coset (1.1) can be thought of as a model with partially fixed κ-symmetry [31, 37]. Where (θ1, φ1) and (θ2, φ2) parametrize two spheres, the angle 0 ≤ ξ < π/2 determines their radii, and the angle 0 ≤ ψ < 2π corresponds to a U(1) isometry
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