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Conformal operators in QCD

Yuri Makeenko

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Abstract

Utilizing the properties of the representations of the conformal group, we obtain new expressions for the conformal operators composed of spinor or scalar fields of arbitrary dimension in terms of Jacobi polynomials. These expressions generalize the known formulas in terms of Gegenbauer polynomials. Using the conformal Ward identities, we prove the multiplicative renormalizability of conformal operators in the leading logarithmic approximation.

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What this paper is about

Utilizing the properties of the representations of the conformal group, we obtain new expressions for the conformal operators composed of spinor or scalar fields of arbitrary dimension in terms of Jacobi polynomials. These expressions generalize the known formulas in terms of Gegenbauer polynomials. Using the conformal Ward identities, we prove the multiplicative renormalizability of conformal operators in the leading logarithmic approximation.

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Available abstract

Utilizing the properties of the representations of the conformal group, we obtain new expressions for the conformal operators composed of spinor or scalar fields of arbitrary dimension in terms of Jacobi polynomials. These expressions generalize the known formulas in terms of Gegenbauer polynomials. Using the conformal Ward identities, we prove the multiplicative renormalizability of conformal operators in the leading logarithmic approximation.

Key concepts: Conformal map, Primary field, Mathematics, Scalar (mathematics), Spinor, Conformal symmetry, Conformal anomaly, Multiplicative function

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