HET Seminar | Valentina Prilepina, Laval University | "Efficient Rules for All Conformal Blocks: A Dream Come True" | via Zoom

Fri, Apr 10, 2020, 1:45 pm

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In this talk, I will lay out a set of efficient rules for computing d-dimensional global conformal blocks in arbitrary Lorentz representations in the context of the embedding space operator product expansion (OPE) formalism. With these rules in place, the general procedure for determining all possible conformal blocks is reduced to (1) identifying the relevant group theoretic quantities and (2) applying the conformal rules to obtain the blocks. The rules represent a systematic prescription for computing the blocks in a convenient mixed OPE-three-point- function basis as well as a set of rotation matrices, which are necessary to translate these blocks to the pure three-point function basis relevant for the conformal bootstrap. I will start by tracing their origin by describing some of the essential ingredients present in the formalism that naturally give rise to these rules. I will then map out the derivation of the rules, first outlining the general algorithm for the rotation matrices and then proceeding to the conformal blocks. Along the way, l will introduce a convenient diagrammatic notation (somewhat reminiscent of Feynman diagrams), which serves to encode parts of the computation in a compact form. Finally, I will treat several interesting examples to demonstrate the application of these rules in practice.