Spinning conformal blocks

By M. Costa, J. Penedones, David Poland, S. Rychkov. 2011

324 citations recorded by the source corpus.

A bstractFor conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

Subfields: Astronomy and Astrophysics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f59e972a521ef03ced1f54fc5277796f607e338d

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Citations in the corpus

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Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “Significant progress in understanding non-scalar conformal partial waves was made recently in [43] (building on [44]), which also contains a concise introduction to the concept.”
Spinning conformal correlators (2011, methodology): “In an upcoming paper [6], we shall use this formalism to obtain conformal blocks for four-point functions of tensor operators.”
Weight shifting operators and conformal blocks (2017, unknown): “5 This generalizes the beautiful result of [70] for conformal blocks of symmetric traceless tensors (STTs).”
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A proof of the conformal collider bounds (2016, methodology): “The general 3-point function 〈V φO〉, where O is a symmetric traceless tensor primary, using the formalism of [55, 56], takes the form”
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The bootstrap program for boundary CFTd (2012, methodology): “We will use the results of [35], see also [36], and adapt them to conformal field theories with a boundary.”
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A semidefinite program solver for the conformal bootstrap (2015, background): “With recent analytical work [34–40], we now understand in principle how to formulate many interesting bootstrap calculations, like studies of four-point functions of scalars, fermions, conserved currents, stress-tensors, and mixed correlators combining all of these ingredients.”
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