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Loops in AdS from conformal field theory [electronic resource].

Published:
Washington, D.C. : United States. Dept. of Energy, 2017.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy
Physical Description:
Article numbers 36 : digital, PDF file
Additional Creators:
Princeton University, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary:
We 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 nite 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 $\phi$4 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 in nite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.
Report Numbers:
E 1.99:1425488
Subject(s):
Other Subject(s):
Note:
Published through SciTech Connect.
07/10/2017.
": 6321"
Journal of High Energy Physics (Online) 2017 7 ISSN 1029-8479 AM
Ofer Aharony; Luis F. Alday; Agnese Bissi; Eric Perlmutter.
Israel Science Foundation
Funding Information:
FG02-91ER40671
1937/12
1200/14
306260
View MARC record | catkey: 23503350