2021/12/14 by Pallab Basu, Basu, Pallab, Pranav Kumar +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Entropy (arrow of time) #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #Geometry #High Energy Physics - Theory (hep-th) #Mathematical physics #Mathematics #Phase transition #Physics #Quantum #Quantum entanglement #Quantum mechanics #Scalar (mathematics) #Scalar curvature #Scalar field #hep-th
paper · pdf · doi:10.48550/arxiv.2112.07750
published in arXiv (Cornell University) (Cornell University) · 38 pages, 16 figures
arxiv created 2021/12/14 · openalex publication_date 2021/12/14 · arxiv updated 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS4 with its spatially compact boundary S2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of \it incomplete C-theorem and an \it incomplete attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Λ) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.