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

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [2];  [2]
  1. Univ. of Oxford (United Kingdom); Stony Brook University
  2. Indian Institute of Science (India). Centre for High Energy Physics
+ Show Author Affiliations
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.
Research Organization:
Stony Brook Univ., NY (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FG02-88ER40388
OSTI ID:
2280782
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2020; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

1/N expansion
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AdS-CFT correspondence
conformal field theory
effective field theories