A note on the functional determinant of higher-derivative scalar fields on sphere products

Autor:	Dowker, J. S.
Rok vydání:	2023
Předmět:	High Energy Physics - Theory Mathematics - Differential Geometry Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	It is shown that the functional determinant ($\sim$ effective action) for a scalar field propagating on the mixed signature product of unit spheres, S$^q\times$S$^p$, according to the GJMS operator, depends, if $d$ is odd, only on $d=p+q$ and on whether $p$ is even or odd. In the first case the effective action equals twice the standard quantity on S$^d$ and vanishes in the second. Comment: 6 pages Conclusion reworded more accurately, Cautionary footnote added re negative eigenvalues. Spelling corrected and minor text changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.12027 Zobrazit plný text záznamu View this record from Arxiv