Searching for a $C$-function on the three-dimensional sphere
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Abstract
We present a detailed analytic study on the three-dimensional sphere of the most popular candidates for $C$-functions, both for Dirac and scalar free massive fields. We discuss to which extent the effective action, the R\'enyi entanglement entropy and the renormalized entanglement entropy fulfill the conditions expected from $C$-functions. In view of the absence of a good candidate in the case of the scalar field, we introduce a new candidate, which we call the modified effective action, and analyze its pros and cons.Keywords
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This publication has 16 references indexed in Scilit:
- Topological entropy and renormalization group flow in 3-dimensional spherical spacesJournal of High Energy Physics, 2015
- A refinement of entanglement entropy and the number of degrees of freedomJournal of High Energy Physics, 2013
- Is renormalized entanglement entropy stationary at RG fixed points?Journal of High Energy Physics, 2012
- The constraints of conformal symmetry on RG flowsJournal of High Energy Physics, 2012
- Rényi entropies for free field theoriesJournal of High Energy Physics, 2012
- On renormalization group flows in four dimensionsJournal of High Energy Physics, 2011
- F-theorem without supersymmetryJournal of High Energy Physics, 2011
- Towards a derivation of holographic entanglement entropyJournal of High Energy Physics, 2011
- c -theorem and spectral representationNuclear Physics B, 1991
- Analogs of the c-theorem for four-dimensional renormalisable field theoriesNuclear Physics B, 1990