2025/04/22 by F. Gliozzi, Gliozzi, Ferdinando · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2504.15904
openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The n-point functions of any Conformal Field Theory (CFT) in d dimensions can always be interpreted as spatial restrictions of corresponding functions in a higher-dimensional CFT with dimension d'> d. In particular, when a four-point function in d dimensions has a known conformal block expansion, this expansion can be easily extended to d'=d+2 due to a remarkable identity among conformal blocks, discovered by Kaviraj, Rychkov, and Trevisani (KRT) as a consequence of Parisi-Sourlas supersymmetry and confirmed to hold in any CFT with d > 1. In this note, we provide an elementary proof of this identity using simple algebraic properties of the Casimir operators. Additionally, we construct five differential operators, Λi, which promote a conformal block in d dimensions to five conformal blocks in d+2 dimensions. These operators can be normalized such that ∑i Λi = 1, from which the KRT identity immediately follows. Similar, simpler identities have been proposed, all of which can be reformulated in the same way.