Spinning AdS propagators

By M. Costa, V. Gonçalves, J. Penedones. 2014

250 citations recorded by the source corpus.

A bstractWe develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also find a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplitude associated to AdS graviton exchange between minimally coupled scalars of general dimension, including the regular part of the amplitude.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1034d1f65abdbb9a4169e9dfeab4c8d3bd867ea4

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Citations in the corpus

Defects in conformal field theory (2016, methodology): “The embedding space machinery was set up for antisymmetric tensors in [46] and for fields living in AdS in [47].”
Nonlinear gravity from entanglement in conformal field theories (2017, methodology): “In this gauge, we can write the Euclidean bulk-to-boundary propagator conveniently using the index-free notation introduced in [37] as”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “This is indeed consistent with the known expressions in the case of totally symmetric tensors considered in [54].”
Celestial amplitudes and conformal soft theorems (2019, unknown): “, [45]).”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, methodology): “Based on this, we expect agreement for general `, although we have not so far succeeded in showing this due to the somewhat complicated form for the general spin-` bulk-to-bulk propagator [65, 66].”
Loops in AdS from conformal field theory (2016, background): “See [14, 15, 26, 27, 56–62] for foundational work, and [22,62–68] for some recent applications, of Mellin space in CFT.”
Bounding the space of holographic CFTs with chaos (2016, background): “47) where s and t are Mellin variables in the conventions of [97], and the quantities q (J) v,w and NJ were defined in (4.”
A Mellin space approach to cosmological correlators (2019, methodology): “[68, 84, 85]):”
Virasoro conformal blocks in closed form (2015, unknown): “1 of [44],”
Conformal basis for flat space amplitudes (2017, unknown): “One orthonormality condition we need for the Hd+1 scalar bulk-to-boundary propagator is [35]: ∫ ∞ −∞ dν μ(ν) ∫ d ~ wG d 2 +iν(p̂1; ~ w)G d 2 −iν(p̂2; ~ w) = δ (p̂1, p̂2) , (3.”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, methodology): “C of [103], and [81, 92] for their application in a similar context.”
A Mellin space approach to the conformal bootstrap (2016, unknown): “These have been explicitly studied in [45].”
Bootstrapping inflationary correlators in Mellin space (2019, methodology): “[62, 63]): Ων(Y1, Y2) = ν2 π ∫ dP Kd 2 +iν (Y1, P )Kd 2−iν (Y2, P ) , (2.”