Dimensional reduction for conformal blocks. (English) Zbl 1390.81516
Summary: We consider the dimensional reduction of a CFT, breaking multiplets of the \(d\)-dimensional conformal group \(SO(d+1, 1)\) up into multiplets of \(SO(d,1)\). This leads to an expansion of \(d\)-dimensional conformal blocks in terms of blocks in \(d-1\) dimensions. In particular, we obtain a formula for 3\(d\) conformal blocks as an infinite sum over \(_{2}F_{1}\) hypergeometric functions with closed-form coefficients.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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