Loops in AdS from conformal field theory

By O. Aharony, L. Alday, A. Bissi, Eric Perlmutter. 2016

221 citations recorded by the source corpus.

A bstractWe propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ff2a9be059b8c5689fc0d73071666cccdcca8f6c

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Citations in the corpus

$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, methodology): “In [1], the double-discontinuity of the 1-loop amplitude was derived to order λ− 5 2 in terms of the constants c1 and c2, following a similar derivation for the 1-loop SUGRA term in [50, 76, 77].”
How to succeed at holographic correlators without really trying (2017, background): “At the loop level, impressive progress has been made recently by several authors [45, 75, 80, 81] and it will be interesting to push this program using the insights of our methods.”
All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry (2018, methodology): “Interestingly, in analogy with the unitarity method for one-loop S-matrices [30], “squaring” this tree-level four-point data gives sufficient information to go to one-loop [31], as has now been successfully carried out for low spherical harmonics [32–34].”
Analyticity in spin in conformal theories (2017, unknown): “(A similar conclusion was reached recently in Mellin space [41].”
Bootstrapping inflationary correlators in Mellin space (2019, unknown): “[63, 124, 140–144]).”