AdS field theory from conformal field theory

Fitzpatrick, A. Liam; Kaplan, Jared

doi:10.1007/jhep02(2013)054

AdS field theory from conformal field theory

Journal Article · Mon Feb 11 00:00:00 EST 2013 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2013)054· OSTI ID:1878212

Fitzpatrick, A. Liam ^[1]; Kaplan, Jared ^[2]

Stanford Univ., CA (United States); SLAC
SLAC National Accelerator Lab., Menlo Park, CA (United States); Johns Hopkins Univ., Baltimore, MD (United States)

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative ‘1/N’ expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well- approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg’s soft theorems to AdS/CFT. The AdS analog of Weinberg’s argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1878212

Report Number(s):: SLAC-PUB-17076

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2013; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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