Abstract
We initiate an exploration of the conformal bootstrap for n>4 point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-Abelian conformal gauge theories as their locations approach the cusps of a null polygon. For that we consider consistency of the OPE in the so-called snowflake channel with respect to cyclicity transformations which leave the null configuration invariant. For general non-Abelian gauge theories this allows us to strongly constrain the OPE structure constants of up to three large spin J_{j} operators (and large polarization quantum number l_{j}) to all loop orders. In N=4 we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon, and Papathanasiou.
Highlights
Introduction.—The numerical conformal bootstrap [1] is a well-established physics tool, often leading to the best determination of critical exponent relevant for realworld experiments
We initiate an exploration of the conformal bootstrap for n > 4 point correlation functions
In N 1⁄4 4 we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon, and Papathanasiou
Summary
Ε is a polarization vector and we should only keep the leading terms in x212 This operator identity can be used to derive integral representations for conformal blocks by applying it once, twice, or three times in a 4, 5, and 6 point correlator, respectively. After these multiple OPEs end up with the conformal block as the action of a few 1F1 operators on a spinning 3 point function which in turn is completely fixed by conformal symmetry [14]: hOðx; ε1Þ...Oðx; ε3Þi. X2ij ≡ ðxi − xjÞ2; ð6Þ while all other four cross ratios are trivially obtained by shifting the indices here, ui ≡ ui−1jxi→xiþ ; ð7Þ where i 1⁄4 2, 3, 4, 5; see Fig. 1. The leading twist blocks simplify dramatically into a simple product of Bessel functions
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