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Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs

Ferrero, P and Ghosh, K and Sinha, A and Zahed, A (2020) Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs. In: Journal of High Energy Physics, 2020 (7).

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Official URL: https://dx.doi.org/10.1007/JHEP07(2020)170


We develop the technology for Polyakov-Mellin (PM) bootstrap in one- dimensional conformal field theories (CFT1). By adding appropriate contact terms, we bootstrap various effective field theories in AdS2 and analytically compute the CFT data to one loop. The computation can be extended to higher orders in perturbation theory, if we ignore mixing, for any external dimension. We develop PM bootstrap for O(N) theories and derive the necessary contact terms for such theories (which also involves a new higher gradient contact term absent for N = 1). We perform cross-checks which include considering the diagonal limit of the 2d Ising model in terms of the 1d PM blocks. As an independent check of the validity of the results obtained with PM bootstrap, we propose a suitable basis of transcendental functions, which allows to fix the four-point correlators of identical scalar primaries completely, up to a finite number of ambiguities related to the number of contact terms in the PM basis. We perform this analysis both at tree level (with and without exchanges) and at one loop. We also derive expressions for the corresponding CFT data in terms of harmonic sums. Finally, we consider the Regge limit of one-dimensional correlators and derive a precise connection between the latter and the large-twist limit of CFT data. Exploiting this result, we study the crossing equation in the three OPE limits and derive some universal constraints for the large-twist limit of CFT data in Regge-bounded theories with a finite number of exchanges. © 2020, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer
Additional Information: Copy right for this article belongs to Springer
Keywords: 1/N Expansion, AdS-CFT Correspondence, Conformal Field Theory, E�ective Field Theories
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 28 Oct 2020 09:27
Last Modified: 28 Oct 2020 09:27
URI: http://eprints.iisc.ac.in/id/eprint/66157

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