2020/06/30 by Sera Cremonini, Li Li, Kyle Ritchie +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Geometry #Lorentz covariance #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Renormalization group #Scalar (mathematics) #Superpotential #Supersymmetry #Theoretical physics #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevd.103.046006
published as Phys. Rev. D 103, 046006 (2021) · 34 pages, 8 figures. Minor comments added and references added
arxiv created 2020/09/10 · openalex publication_date 2021/02/09 · arxiv updated 2021/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We examine nonrelativistic holographic renormalization group (RG) flows by working with Einstein-Maxwell-scalar theories which support geometries that break Lorentz invariance at some energy scale. We adopt the superpotential formalism, which helps us characterize the radial flow in this setup and bring to light a number of generic features. In particular, we identify several quantities that behave monotonically under RG flow. As an example, we show that the index of refraction is generically monotonic. We also construct a combination of the superpotentials that flows monotonically in Einstein-scalar theories supporting nonrelativistic solutions and which reduces to the known c-function in the relativistic limit. Interestingly, such quantity also exhibits monotonicity in a variety of black hole solutions to the full Einstein-Maxwell-scalar theory, hinting at a deeper structure. Finally, we comment on the breakdown of such monotonicity conditions and on the relation to a candidate c-function obtained previously from entanglement entropy.