New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
By S. Raju. 2012
196 citations recorded by the source corpus.
We consider correlation functions of the stress-tensor or a conserved current in AdS_{d+1}/CFT_d computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree level. These relations have an advantage over the BCFW-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the d-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon or graviton amplitude appears as its coefficient.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/da70b38d568b3aa4b5a23b5e3a6f46d7ab76f3d2
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Citations in the corpus
- CMB from CFT (2012, background): “ Another Argument for Uniqueness Now, we give a second argument — which does not assume the OPE — for why only the choice n 1 = 1,n 2 = 1 is allowed. This argument closely follows an argument made in [18].We will show that any correlator that arises from a local interaction in de Sitter space, in th”
- Implications of conformal invariance in momentum space (2013, unknown): “, [29, 49, 50]).”
- The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “In this limit, we expect the correlator to have a singularity with a coefficient that is related to the flat-space scattering amplitude [24, 44].”
- The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “(See [13–34] for other studies on conformal correlators in momentum space.”
- Building a boostless bootstrap for the bispectrum (2020, background): “• Rule 3: For any n-point correlatorBn, the residue of the total energy pole kT ≡ ∑n a=1 ka → 0 is related to a corresponding amplitude An by [6, 28, 27]”
- Bootstrapping inflationary correlators in Mellin space (2019, unknown): “[41, 42, 125–130].”
- The Cosmological Optical Theorem (2020, background): “It has been observed [6, 7] and later discussed e.”
- How to succeed at holographic correlators without really trying (2017, unknown): “A BCFW-inspired formalism for holographic correlators has been developed in momentum space [82, 83].”
- Cosmological Polytopes and the Wavefunction of the Universe (2017, background): “After all seeing “emergent quantum mechanics and space-time” in non-gravitational scattering amplitudes is a luxury, not a necessity, but the situation is entirely different in cosmology, where espe1A similar phenomenon occurs for AdS correlators, [3, 4].”
- Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “A momentum space-based approach can be found in [63,64].”
- A Mellin space approach to cosmological correlators (2019, background): “[8, 9, 38–42].”
- The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, background): “The study of cosmological correlators has not yet had its Parke–Taylor moment, but the fact that scattering amplitudes live inside cosmological correlators [42, 59] strongly suggests that similar structures exist.”