2014/06/30 by M. Asorey, C. G. Beneventano, I. Cavero-Peláez +3 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Entropy (arrow of time) #Fixed point #Holonomy #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Monotonic function #Renormalization group #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep01(2015)078
published in Journal of High Energy Physics 2015(1) (Springer Nature) · 35 pages, 5 figures. Minor changes; matches published version
openalex publication_date 2015/01/01 · arxiv created 2015/01/17 · arxiv updated 2015/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit β/a ≪ 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than (2π )/(β ) , this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top > S top . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F -theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces.