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arXiv · 1705.00071

Searching for a $C$-function on the three-dimensional sphere

C. G. Beneventano·I. Cavero-Peláez·D. D'Ascanio·E. M. Santangelo
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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 Rényi 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.

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C. G. Beneventano, I. Cavero-Peláez, D. D'Ascanio, E. M. Santangelo. 2017-04-28. Searching for a $C$-function on the three-dimensional sphere. https://doi.org/10.1088/1751-8121%2Faa8e38

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