Crossing symmetry and Higher spin towers

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.

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Simplifying large spin bootstrap in Mellin space

Dey

Ghosh

Sinha

2018

“…By looking at specific terms in this equation order by order in u, we are able to fix the CFT data of the quadrilinear operators. 13 Specifically, we fix:…”

Section: Quadrilinearsmentioning

confidence: 99%

“…From the above, we see that any terms log J J 2m with m 2 will contain divergences of the form log 3 v, and must therefore be discarded. We focus on the log u log v part of the crossing equation: 13) and specifically terms of the form…”

Section: Couplingmentioning

confidence: 99%

The analytic bootstrap in fermionic CFTs

Loon

2018

Abstract:We apply the method of the large spin bootstrap to analyse fermionic conformal field theories with weakly broken higher spin symmetry. Through the study of correlators of composite operators, we find the anomalous dimensions and OPE coefficients in the GrossNeveu model in d = 2 + ε dimensions and the Gross-Neveu-Yukawa model in d = 4 − ε dimensions, based only on crossing symmetry. Furthermore a non-trivial solution in the d = 2 + ε expansion is found for a fermionic theory in which the fundamental field is not part of the spectrum. The results are perturbative in ε and valid to all orders in the spin, reproducing known results for operator dimensions and providing some new results for operator dimensions and OPE coefficients.

“…Double-trace induced Gamma functions are omnipresent in holographic calculations and enter very naturally in the Mellin integrands of CFT/AdS correlators [1][2][3]. It would be fascinating to establish a connection with the integrability formulae found here by con- 24 Similar formulae were also found at weak coupling in the large spin limit [39,42] using conformal bootstrap ideas. They hold when Γcusp ∼ 0 for a flux-tube energy γ ∼ 2Γcusp log S = O(1).…”

Section: Resultsmentioning

confidence: 65%

Three-point functions at strong coupling in the BMN limit

Basso

Zhong

2020

We consider structure constants of single-trace operators at strong coupling in planar N = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavylight correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.