Abstract
We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.
Highlights
We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3 × S3, with two operators in tensor multiplet and the other two in gravity multiplet
After factoring out(z − z), we can formally express sk1 sk2 σk3 σk4 in Mellin space using the standard definition in (2.5), and the recursion relation can be solved in a similar manner as for the correlators of tensor multiplet that we studied in the previous section
We present compact formulas for all four-point tree-level holographic correlators in AdS3 × S3 in supergravity limit, with all the operators in tensor multiplet, as well as for the mixed correlators where we have two operators in tensor multiplet and the other two in gravity multiplet
Summary
We will consider the correlators involving operators in gravity multiplet. As we commented, compared to the correlators of operators in tensor multiplet, these correlators are more involved. For the comparison of holographic correlators in AdS3, we compactify the above amplitude to three dimensions This is done by reducing the 6D spinors to 3D spinor, which effectively sets [1−2−3+4+] = − 12 34 , where in 3D, the massless momentum can be expressed as pαi β = λαi λβi , and the angle braket is defined as ij = λαi λβj αβ, which relates to Mandelstam variables by ij 2 = (pi + pj). When compactified to 4D, the (2, 0) supergravity becomes supersymmetric multiple-U(1) Einstein-Maxwell theory Both the scalar arising from the 6D graviton multiplet and the scalar from the 6D tensor multiplet are matters of Einstein-Maxwell theory [33], but they belong to different U(1)’s of Maxwell theory, they do not couple to a 4D graviton, which reflects in (3.4) by the fact that there are no t- or u-channel poles. This fact implies only the s-channel pole is allowed, and a further reduction to 3D does not change the structure
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