2024/04/23 by Rodrigo Aros, F. Bugini, Aros, R. +5
Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Radioactive Decay and Measurement Techniques
paper · pdf · doi:10.48550/arxiv.2404.15561
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We elucidate the dependence of the Casimir energy on the trace anomaly coefficients for a six-dimensional CFT on R× S5. This extends the universal dependence on the central charge in 2D and the relation by Cappelli and Coste in 4D, unveiling the role of the trivial total derivatives in the anomaly that renders the Casimir energy scheme dependent. We obtain Eo=-(15)/(8) a6 -(5)/(12) (g5+(1)/(4) g7+(1)/(2) g8-10 g9+g10), with a6 being the type A central charge and the g's, the coefficients of five out of six terms that form a basis for trivial total derivatives. The derivation is based on the Polyakov formulas (conformal primitive) resulting from the integration of the trace anomaly. Alternatively, on a 6D conformally flat background the above basis is redundant and one can simplify further to get, in terms of the Schouten scalar J and the Schouten tensor V, Branson's basis for trivial total derivatives ∇2∇2 J, ∇2J2 and ∇2|V|2+2∇⋅(V⋅∇ J) with coefficients γ1, γ2 and γ3, respectively, Eo=-(15)/(8)a6-(1)/(24)(γ1-γ2 -(1)/(8)γ3)~.