Towards spinning Mellin amplitudes

In this paper, we propose a p-adic analog of Mellin amplitudes for scalar operators, and present the computation of the general contact amplitude as well as arbitrary-point tree-level amplitudes for bulk diagrams involving up to three internal lines, and along the way obtain the p-adic version of the split representation formula. These amplitudes share noteworthy similarities with the usual (real) Mellin amplitudes for scalars, but are also significantly simpler, admitting closed-form expressions where none are available over the reals. The dramatic simplicity can be attributed to the absence of descendant fields in the p-adic formulation.

“…Refs. [32,65,66,33,67,68,69]. On the p-adic front, however, it is at present not well understood how to describe spinning degrees of freedom in a discrete bulk geometry.…”

Section: Discussionmentioning

confidence: 99%

p-adic Mellin amplitudes

Jepsen

Parikh

2019

“…The correlator G(ξ r ) conn is captured by the function M (δ ij ) which is the reduced Mellin amplitude following Mack's terminology. 4 For other applications and recent developments, see [1,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]). 5 More generally, the number of independent cross ratios is nd − 1 2 (d + 1)(d + 2) if n d + 1 and 1 2 n(n − 3) if n < d + 1.…”

Section: Mellin Representationmentioning

confidence: 99%

On superconformal four-point Mellin amplitudes in dimension d > 2

Zhou

2018

187

We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for SCFT d with 3 ≤ d ≤ 6. This leads to a new technique to compute holographic correlators, which is similar but complementary to the ones introduced in [1, 2]. We apply this technique to theories in various spacetime dimensions. In addition to reproducing known results, we obtain a simple expression for next-next-to-extremal fourpoint functions in AdS 7 × S 4 . We also use this machinery on AdS 4 × S 7 and compute the first holographic one-half BPS four-point function. We extract the anomalous dimension of the R-symmetry singlet double-trace operator with the lowest conformal dimension and find agreement with the 3d N = 8 numerical bootstrap bound at large central charge.

“…σs + r and c = 3 2 + iσ s ν, we can express the three dimensional scalar conformal partial waves in terms of an infinite summation over Legendre polynomials. More explicitly we have: 39) and notice that we have used the fact C…”

Section: Conformal Blocks With Integer Spin and Appell's Hypergeometrmentioning

confidence: 99%

On conformal blocks, crossing kernels and multi-variable hypergeometric functions

Chen

Kyono

2019

Self Cite

In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function F 4 . We also construct its generalization to the non-local primary exchange operator with continuous spin and its corresponding Mellin representation which are relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute the so-called crossing kernel in general spacetime dimensions, the resultant expression can be written as a double infinite summation over certain Kampé de Fériet hypergeometric functions with the correct double trace operator singularity structures. We also include some complementary computations in AdS space, demonstrating the orthogonality of conformal blocks and performing the decompositions.