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Loops in AdS from conformal field theory

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4]
  1. Weizmann Inst. of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics; Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
  2. Univ. of Oxford (United Kingdom). Mathematical Inst.
  3. Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
  4. Princeton Univ., NJ (United States). Dept. of Physics
+ Show Author Affiliations
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.
Research Organization:
Trustees of Princeton Univ., NJ (United States)
Sponsoring Organization:
Israel Science Foundation; USDOE
Grant/Contract Number:
FG02-91ER40671
OSTI ID:
1425488
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2017; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (66)

Quantum gravity from conformal field theory journal January 2018
A study of quantum field theories in AdS at finite coupling journal January 2019
Unmixing supergravity journal February 2018
Quantum ϕ4 theory in AdS4 and its CFT dual journal February 2019
The analytic functional bootstrap. Part II. Natural bases for the crossing equation journal February 2019
Polyakov-Mellin bootstrap for AdS loops journal February 2020
Bootstrapping inflationary correlators in Mellin space journal February 2020
Mellin amplitudes for fermionic conformal correlators journal March 2018
How to succeed at holographic correlators without really trying journal April 2018
p-adic Mellin amplitudes journal April 2019
Loop corrections for Kaluza-Klein AdS amplitudes journal May 2018
Recursion relations in Witten diagrams and conformal partial waves journal May 2019
Holographic dual of the five-point conformal block journal May 2019
Spinning AdS loop diagrams: two point functions journal June 2018
Solving M-theory with the conformal bootstrap journal June 2018
Genus-one string amplitudes from conformal field theory journal June 2019
A crossing-symmetric OPE inversion formula journal June 2019
Leading order anomalous dimensions at the Wilson-Fisher fixed point from CFT journal July 2017
AdS4/CFT3 for unprotected operators journal July 2018
On Mellin amplitudes in SCFTs with eight supercharges journal July 2018
Higher spin ANEC and the space of CFTs journal July 2019
Holographic reconstruction of AdS exchanges from crossing symmetry journal August 2017
c-Recursion for multi-point superconformal blocks. NS sector journal August 2018
The M-theory S-matrix from ABJM: beyond 11D supergravity journal August 2018
M-theory reconstruction from (2,0) CFT and the chiral algebra conjecture journal August 2018
On superconformal four-point Mellin amplitudes in dimension d > 2 journal August 2018
Growing extra dimensions in AdS/CFT journal August 2019
Analyticity in spin in conformal theories journal September 2017
Operator bases, S-matrices, and their partition functions journal October 2017
Veneziano amplitude of Vasiliev theory journal October 2018
The conformal bootstrap at finite temperature journal October 2018
AdS3× S3 tree-level correlators: hidden six-dimensional conformal symmetry journal October 2019
20′ five-point function from AdS5× S5 supergravity journal October 2019
Propagator identities, holographic conformal blocks, and higher-point AdS diagrams journal October 2019
Conformal bootstrap in the Regge limit journal December 2017
Gravitational S-matrix from CFT dispersion relations journal December 2018
On the Polyakov-Mellin bootstrap journal December 2018
Recursion relations in p  -adic Mellin Space journal June 2019
Large Spin Perturbation Theory for Conformal Field Theories journal September 2017
Loop Corrections to Supergravity on AdS 5 × S 5 journal October 2017
Loops in Anti–de Sitter Space journal September 2018
Handling Handles: Nonplanar Integrability in N = 4 Supersymmetric Yang-Mills Theory journal December 2018
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT text January 2016
Analyticity in Spin in Conformal Theories text January 2017
Holographic Reconstruction of AdS Exchanges from Crossing Symmetry text January 2017
Conformal Bootstrap in the Regge Limit text January 2017
Quantum Gravity from Conformal Field Theory text January 2017
Unmixing Supergravity text January 2017
Operator bases, $S$-matrices, and their partition functions text January 2017
How to Succeed at Holographic Correlators Without Really Trying text January 2017
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Solving M-theory with the Conformal Bootstrap text January 2017
The Conformal Bootstrap at Finite Temperature text January 2018
On Mellin Amplitudes in SCFTs with Eight Supercharges text January 2018
M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture text January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018
c-Recursion for multi-point superconformal blocks. NS sector text January 2018
A Study of Quantum Field Theories in AdS at Finite Coupling text January 2018
Polyakov-Mellin Bootstrap for AdS loops text January 2018
Recursion Relations in Witten Diagrams and Conformal Partial Waves text January 2018
A Crossing-Symmetric OPE Inversion Formula text January 2018
Holographic dual of the five-point conformal block text January 2019
Growing Extra Dimensions in AdS/CFT text January 2019
Bootstrapping Inflationary Correlators in Mellin Space text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AdS-CFT Correspondence
Conformal Field Theory
Gauge-gravity correspondence
Scattering Amplitudes