Abstract
In a class of 2D CFTs with higher spin symmetry, we compute thermal two-point functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge. These are shown to agree with the same quantity calculated holographically using scalar fields propagating in a charged black hole background of 3D higher spin gravity. This match serves as further evidence for the duality between W_N minimal models at large central charge and 3D higher spin gravity. It also supports a recent prescription for computing boundary correlators of multi-trace scalar primary operators in higher spin theories.
Highlights
In a class of 2D CFTs with higher spin symmetry, we compute thermal twopoint functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge
We focus on the non-supersymmetric duality proposals of [2, 3], which state that the WN minimal models in certain large central charge limits, parameterized by a constant λ, are dual to the bosonic 3D higher spin theories of [4] with a single complex scalar field
As we have argued here, the deformation should be given by (3.2). While this is very natural for various reasons, it is not obviously the same as the prescription that was used for the successful match of the black hole and boundary entropies in [13, 14]
Summary
The hs[λ] black hole has a useful zero temperature limit, in which we take τ2 → ∞, α → ∞ for fixed μ = α/τ. The resulting connection is a = V12dz − μV23dza = V−21dz. This has been referred to as the ‘chiral deformation’ background in [16, 20]. Its simplicity will allow us to check scalar correlators in the black hole background against independent calculations in the above limit
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