2017/09/30 by Parijat Dey, Kausik Ghosh, Aninda Sinha · 53 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal anomaly #Conformal field theory #Conformal map #Conformal symmetry #Dimension (graph theory) #Inverse #Mathematical functions and polynomials #Operator product expansion #Polynomial #Space (punctuation) #TRACE (psycholinguistics) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1007/jhep01(2018)152
published in Journal of High Energy Physics 2018(1) (Springer Nature) · 48 pages, 6 figures, typos corrected, to appear in JHEP
openalex created_date 2017/09/25 · openalex publication_date 2018/01/01 · arxiv created 2018/01/22 · arxiv updated 2018/03/14 · openalex updated_date 2026/08/05
We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel. The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Nørlund) polynomials and the Mack polynomials and enable us to derive certain universal properties. Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation. At the next order, the polynomial ambiguity in the Witten diagram basis is needed for the equivalence and we derive the necessary constraints for the same.