2011/07/31 by Marco Baggio, Jan de Boer, Kristian Holsheimer · 62 citations
Mathematics · Physics and Astronomy · #Action (physics) #Anomaly (physics) #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Classical mechanics #Conformal anomaly #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Hamilton–Jacobi equation #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Renormalization #Spacetime #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep01(2012)058
published in Journal of High Energy Physics 2012(1) (Springer Nature) · 27 pages; minor improvements, references added, published version
openalex publication_date 2012/01/01 · arxiv created 2012/09/12 · arxiv updated 2012/09/13 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order to make the on-shell value of the bulk action finite. We study these counterterms using the Hamilton-Jacobi method. Rather than imposing boundary conditions from the start, we will derive suitable boundary conditions by requiring that divergences can be canceled using only local counterterms. We will demonstrate in examples that this procedure indeed leads to a finite bulk action while at the same time it determines the asymptotic behavior of the fields. This puts more substance to the belief that Lifshitz spacetimes are dual to well-behaved field theories. As a byproduct, we will find the analogue of the conformal anomaly for Lifshitz spacetimes.