Topological entropy and renormalization group flow in 3-dimensional spherical spaces

Asorey, M. (Universidad de Zaragoza) ; Beneventano, C.G. ; Cavero-Peláez, I. ; D'Ascanio, D. ; Santangelo, E.M.

Resumen: We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit ß/a « 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than 2p/ß , 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 UV¿>¿S 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 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.

Idioma: Inglés

DOI: 10.1007/JHEP01(2015)078

Año: 2015

Publicado en: Journal of High Energy Physics 2015, 1 (2015), [35 pp]
ISSN: 1126-6708

Factor impacto JCR: 6.023 (2015)

Categ. JCR: PHYSICS, PARTICLES & FIELDS rank: 4 / 28 = 0.143 (2015) - Q1 - T1

Factor impacto SCIMAGO: 1.343 - Nuclear and High Energy Physics (Q1)

Tipo y forma: Article (Published version)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)