Conformal four-point correlation functions from the operator product expansion. (English) Zbl 1454.81187
Summary: We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in [the authors, J. High Energy Phys. 2020, No. 6, Paper No. 28, 87 p. (2020; Zbl 1437.81038)] and present several explicit examples of blocks derived via this method. The procedure for obtaining the blocks has been reduced to (1) determining the relevant group theoretic structures and (2) applying appropriate predetermined substitution rules. The most transparent expressions for the blocks we find are expressed in terms of specific substitutions on the Gegenbauer polynomials. In our examples, we study operators which transform as scalars, symmetric tensors, two-index antisymmetric tensors, as well as mixed representations of the Lorentz group.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 22E43 | Structure and representation of the Lorentz group |
| 62P35 | Applications of statistics to physics |
Citations:
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