Bulk locality for scalars and fermions with global symmetry

Chowdhury, Subham Dutta; Ghosh, Kausik

doi:10.1007/jhep10(2021)146

Cited by 2 publications

(1 citation statement)

References 56 publications

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“…Our results are hence applicable to these cases (see e.g. [44]). However when fermions or unequal scalars are involved the conformal blocks are different, and also we may lose full crossing (anti)symmetry.…”

Section: Fermionic/multiple Correlator Bootstrap: Crossing Antisymmetry Also Appears In In-mentioning

confidence: 60%

Crossing antisymmetric Polyakov blocks + dispersion relation

Kaviraj

2022

J. High Energ. Phys.

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Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the ‘+ type Polyakov blocks’. These blocks are built from AdSd+1 Witten diagrams. In 1d they encode the ‘+ type’ analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent ‘locality constraints’ in addition to the usual CFT sum rules given by the ‘Polyakov conditions’. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

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Section: Fermionic/multiple Correlator Bootstrap: Crossing Antisymmetry Also Appears In In-mentioning

confidence: 60%

Crossing antisymmetric Polyakov blocks + dispersion relation

Kaviraj

2022

J. High Energ. Phys.

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A Celestial route to AdS bulk locality

Bhat,

Zahed

2023

J. High Energ. Phys.

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We prove a precise form of AdS bulk locality by deriving analytical two-sided bounds on bulk Wilson coefficients. Our bounds are on the Wilson coefficients themselves, rather than their ratios, as is typically found in the literature. Inspired by the Celestial amplitudes program in flat space, we perform a Celestial transform of the CFT Mellin amplitude of four identical scalars. Using the crossing symmetric dispersion relation (CSDR), we express the resulting amplitude in terms of crossing symmetric conformal partial waves. The partial waves satisy remarkable positivity properties which along with the unitarity of the CFT prove sufficient to derive the bounds. We then employ our methods in the limit of large AdS radius and recover known bounds on flat space Wilson coefficients and new bounds on their large radius corrections. We check that the planar Mellin amplitude of four stress-tensor multiplets in $$ \mathcal{N} $$ N = 4 SYM satisfies our bounds. Finally, using null constraints, we derive a form of low-spin dominance in AdS EFTs. We find that the low-spin dominance is strongest in flat space and weakens as we move away from flat space towards higher AdS curvature.

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Bulk locality for scalars and fermions with global symmetry

Cited by 2 publications

References 56 publications

Crossing antisymmetric Polyakov blocks + dispersion relation

Crossing antisymmetric Polyakov blocks + dispersion relation

A Celestial route to AdS bulk locality

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