Analyticity and the holographic S-matrix

By A. Fitzpatrick, Jared Kaplan. 2011

219 citations recorded by the source corpus.

A bstractWe derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e8d3427bcb1b86d9dba9dd21d65e28a2dc45457d

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Citations in the corpus

The analytic bootstrap and AdS superhorizon locality (2012, background): “Thus far much of the work on the bootstrap has been numerical and has focused on questions of phenomenological interest, so further studies of superconformal theories [12], AdS/CFT setups [10], and even quantum gravity [41] may yield important results.”
Bootstrapping the O(N ) vector models (2013, background): “The sum over poles may also be particularly interesting from the perspective of Mellin amplitudes [58–66].”
Causality constraints in conformal field theory (2015, background): “The story for scalars, initiated in [23] and developed for example in [16, 24–33], is that effective field theories in the bulk are in one-to-one correspondence with solutions of crossing symmetry in CFT, order by order in 1/N .”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “39 See, for example, [333] for a discussion of locality in holographic duality, and [334] for an interesting spin of the problem.”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, methodology): “Using crossing symmetry and the analytic structure of tree-level Witten diagrams in Mellin space [32–35], we can then expand Mp(s, t) as a series in 1/λ: Mp =c−1 ( B 1Mp + λ− 3 2 [ B 4Mp +B 1Mp ] + λ−2 [ B 5Mp +B 4Mp +B 1Mp ] + λ− 5 2 [ B 6,1M p +B 6,2M p +B 5Mp +B 4Mp +B 1Mp ] +O(λ−3) ) +O(c−2) .”
Loops in AdS from conformal field theory (2016, methodology): “This is the one case where M1−loop is actually known directly from a bulk calculation, performed in Mellin space in [26]: the authors used an AdS analog of the Källén-Lehmann representation to write the loop as an infinite sum of trees.”
New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators (2012, background): “he boundary stress tensor correlator? This question was addressed in the early days of AdS/CFT — albeit in a somewhat formal manner (see [14] and references there) — and more recently in Mellin space [11, 15] where several explicit results were obtained. However, extending an observation ﬁrst made f”
Conformal Regge theory (2012, background): “They are very convenient because they make manifest the analogy between scattering amplitudes and conformal correlation functions [10, 11, 12, 13, 14, 15, 16].”
The S-matrix bootstrap. Part I: QFT in AdS (2016, methodology): “The corresponding loop diagram in AdS can be computed with the use of the following identity [19]”
Bootstrapping inflationary correlators in Mellin space (2019, background): “The Mellin space representation of conformal correlators [5–13] and Harmonic Analysis for the Euclidean Conformal Group [12, 14–17] have proven instrumental in making this connection manifest, which encode bulk physics in a way which shares key similarities with the flat-space scattering amplitudes.”
Bootstrapping mixed correlators in the 3D Ising model (2014, background): “Other recent studies of global conformal blocks can be found in [12, 45, 46, 51, 52, 55–61], with connections to Mellin amplitudes in [62–71].”
Projectors, shadows, and conformal blocks (2012, background): “This procedure can be performed quickly and elegantly in Mellin space [37], but takes some care in position space.”
A Mellin space approach to cosmological correlators (2019, unknown): “In position space, the Mellin representation for Witten diagrams [31–33] has already stood out as an indispensable tool which moreover makes manifest the analogy between AdS correlators and flat space scattering amplitudes [34–37].”
4D scattering amplitudes and asymptotic symmetries from 2D CFT (2016, background): “This ambitious goal has a long history [8–16], typically with a focus on AdS/CFT in the limit of infinite AdS radius.”
How to succeed at holographic correlators without really trying (2017, background): “A precise prescription for relating the massless17 flat-space scattering amplitude T (Ki) to the asymptotic form of the holographic Mellin amplitude was given in [41] and justified in [71], M(δij) ≈ Rn(1−d)/2+d+1 Γ(12 ∑ i ∆i − d 2) ∫ ∞”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “Let us study these issues in more detail, and then we will formulate some general, su(cid:14)cient criteria for thermality, motivated in part by our present understanding [9{11, 13, 55{57] of the relationship between CFT data and AdS locality.”
Unitarity and the holographic S-Matrix (2011, methodology): “An elementary feature of the AdS/CFT correspondence is that AdS global time (1)We reviewed aspects of CFT physics and the Mellin amplitude in our recent companion paper [9], and we discussed them in detail in [7], so we urge interested readers to consult these references for a review.”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “3 Relation to Mellin space It is worth noting that the spin-` conformal block has a Mellin representation with exponential dependence on the Mellin parameter: up to normalization [24],”
Operator product expansion convergence in conformal field theory (2012, background): “and not-too-high spin l operators was discussed in [30].”
OPE Convergence in Conformal Field Theory (2012, background): “and not-too-high spin l operators was discussed in [30].”