Conformal Correlation functions in four dimensions from Quaternionic Lauricella system

Abstract

Correlation functions in Euclidean conformal field theories in four dimensions are expressed as representations of the conformal group $SL(2,\stackrel{˝}{)}$, $\H$ being the field of quaternions, on the configuration space of points. The representations are obtained in terms of Lauricella system for quaternions. It generalizes the two-dimensional case, wherein the $N$-point correlation function is expressed in terms of solutions of Lauricella system on the configuration space of $N$ points on the complex plane, furnishing representation of the conformal group $SL(2,\C)$.

1+23 pages. Version published in Nuclear Physics B 968 (2021) 115433

References in corpus (3)

• Conformal Bootstrap in Mellin Space
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Yangian Bootstrap for Conformal Feynman Integrals

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• Universal Spinning Casimir Equations and Their Solutions
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey