IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
Autor/es:
M. ASOREY; C.G. BENEVENTANO; I. CAVERO-PELÁEZ; D. D'ASCANIO; E.M. SANTANGELO
Revista:
JOURNAL OF HIGH ENERGY PHYSICS - (Online)
Editorial:
Springer
Referencias:
Año: 2015 vol. 2015 p. 78 - 113
ISSN:
1029-8479
Resumen:
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit $eta/a ll 1$ of a massive field theory in 3-dimensional  spherical  spaces, $M_3$, with constant curvature $6/a^2$.For masses  lower  than $rac{2pi}{eta}$, this term can be identified with the free energy ofthe same theory on  $M_3$ considered as a  3-dimensional  Euclidean space-time.The non-extensive part of this free energy, $S_{ m hol}$, is generated by the holonomy ofthe spatial metric connection. We show that for homogeneous spherical spaces theholonomy entropy $S_{ m hol}$ decreases monotonically when the RG scale flows to theinfrared.  At the conformal fixed points  the values of the holonomy entropy do coincide with thegenuine 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. $S_{ m top}^{UV}>S_{ m top}^{IR}$. 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 ofthe  2-dimensional  $c$-theorem  and  the 4-dimensional $a$-theorem. The conjecture is related to  recent formulations of the$F$-theorem. In particular, the holonomyentropy on lens spaces is directly related to the topological Rényi entanglement entropy ondisks of 2-dimensional flat spaces.