Topological entropy and renormalization group flow in 3-dimensional spherical spaces
Abstract: 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<sub>3</sub>, with constant curvature 6/a<sup>2</sup>. For masses lo...
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2015
|
| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/86010 |
| Aporte de: |
| id |
I19-R120-10915-86010 |
|---|---|
| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Ciencias Exactas Física Conformal and W Symmetry Discrete and Finite Symmetries Renormalization Group |
| spellingShingle |
Ciencias Exactas Física Conformal and W Symmetry Discrete and Finite Symmetries Renormalization Group Asorey, M. Beneventano, Carlota Gabriela Cavero Peláez, I. D'Ascanio, Daniela Santángelo, Eve Mariel Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| topic_facet |
Ciencias Exactas Física Conformal and W Symmetry Discrete and Finite Symmetries Renormalization Group |
| description |
Abstract: 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<sub>3</sub>, with constant curvature 6/a<sup>2</sup>. For masses lower than 2π/β, this term can be identified with the free energy of the same theory on M<sub>3</sub> considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S<sub>hol</sub>, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S<sub>hol</sub> 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<SUP>UV</SUP><sub>top</sub> > S<SUP>IR</SUP><sub>top</sub>. 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. |
| format |
Articulo Articulo |
| author |
Asorey, M. Beneventano, Carlota Gabriela Cavero Peláez, I. D'Ascanio, Daniela Santángelo, Eve Mariel |
| author_facet |
Asorey, M. Beneventano, Carlota Gabriela Cavero Peláez, I. D'Ascanio, Daniela Santángelo, Eve Mariel |
| author_sort |
Asorey, M. |
| title |
Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| title_short |
Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| title_full |
Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| title_fullStr |
Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| title_full_unstemmed |
Topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| title_sort |
topological entropy and renormalization group flow in 3-dimensional spherical spaces |
| publishDate |
2015 |
| url |
http://sedici.unlp.edu.ar/handle/10915/86010 |
| work_keys_str_mv |
AT asoreym topologicalentropyandrenormalizationgroupflowin3dimensionalsphericalspaces AT beneventanocarlotagabriela topologicalentropyandrenormalizationgroupflowin3dimensionalsphericalspaces AT caveropelaezi topologicalentropyandrenormalizationgroupflowin3dimensionalsphericalspaces AT dascaniodaniela topologicalentropyandrenormalizationgroupflowin3dimensionalsphericalspaces AT santangeloevemariel topologicalentropyandrenormalizationgroupflowin3dimensionalsphericalspaces |
| bdutipo_str |
Repositorios |
| _version_ |
1764820489210953730 |