The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
Conformal Bootstrap in Mellin Space
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abstract
We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mellin representation of CFT amplitudes. We employ exchange Witten diagrams with built in crossing symmetry as our basic building blocks rather than the conventional conformal blocks in a particular channel. Demanding consistency with the operator product expansion (OPE) implies an infinite set of constraints on operator dimensions and OPE coefficients. We illustrate the power of this method in the epsilon expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and, strikingly, obtaining OPE coefficients to higher orders in epsilon than currently available using other analytic techniques (including Feynman diagram calculations). Our results enable us to get a somewhat better agreement of certain observables in the 3d Ising model, with the precise numerical values that have been recently obtained.
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A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
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Rethinking Dimensional Regularization in Critical Phenomena
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.