Teoría cuántica de campos en espacios esféricos con diversas topologías

Una de las preguntas fundamentales en Teoría Cuántica de Campos se refiere a la determinación de una medida del número de grados de libertad de las teorías que sea consistente con el flujo del grupo de renormalización. La respuesta parece estar cifrada en los llamados teoremas C, que involucran cantidades que decrecen con el flujo hacia el infrarrojo del grupo de renormalización y son estacionarias en los puntos fijos, ordenando el espacio de teorías. En un problema originalmente distinto, inspirados en la utilización de los espacios esféricos en modelos cosmológicos, estudiamos las propiedades termodinámicas de una teoría libre a temperatura finita definida sobre esos espacios. Comenzamos analizando el caso de una teoría escalar conforme: a partir de la regularización zeta de la acción efectiva calculamos la entropía, en cuyo desarrollo a altas temperaturas encontramos un término ---a menudo omitido--- que no depende de la temperatura ni del tamaño del espacio, que puede obtenerse como el determinante de la teoría sin temperatura sobre la variedad espacial, y que asociamos con sus propiedades topológicas. Estudiamos en el caso de una teoría masiva el mismo desarrollo, en el que el término independiente de la temperatura depende de la masa, y encontramos que esa dependencia es la que se espera de una cantidad C. Analizamos el comportamiento de ese término para el flujo de masa de una teoría de Dirac libre, donde encontramos un comportamiento monótono pero opuesto al esperado. En ambos casos estudiamos la estabilidad de la cantidad C en los puntos fijos del flujo. Consideramos además una generalización de estos cálculos a algunos espacios en dimensión arbitraria.Facultad de Ciencias Exacta

Photon Scattering by an Electric Field in Noncommutative Spacetime

As is known, the existence of a small noncommutativity between coordinates would generate nonlocal self-interactions in the electromagnetic theory. To explore some consequences of this effect on the propagation of photons we consider Moyal space half-filled with a static and homogeneous electric field and analyze electromagnetic fluctuations on top of this step-like background. Both the localization of photons and the possibility of photon production by strong electric fields are addressed. Several aspects of the Klein paradox in this setup are discussed as well.Comment: 27 pages, 13 figure

Affine Killing vector fields on homogeneous surfaces with torsion

Many  extensions  of  General  Relativity  are  based  on  considering  metric  and  affine  structures as independent properties of spacetime.  This leads to the possibility of introducing torsion as an independent degree of freedom.  In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional manifolds.  We give a complete description of the Lie algebras of affine Killing vector fields on homogeneous surfaces.  This can be used in the search of non-metrizable surfaces of interest.Fil: D'ascanio, Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Gilkey, Peter. Mathematics Department, University Of Oregon; Estados UnidosFil: González Pisani, Pablo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Renormalization on noncommutative torus

We study a self-interacting scalar φ4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d= 2 and d= 4 , the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.Instituto de Física La Plat

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

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.Instituto de Física La Plat

Affine Killing vector fields on homogeneous surfaces with torsion

Many extensions of general relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional manifolds. We give a complete description of the Lie algebras of affine Killing vector fields on homogeneous surfaces. This can be used in the search of non-metrizable surfaces of interest.Instituto de Física La Plat

Renormalization on noncommutative torus

We study a self-interacting scalar φ4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d= 2 and d= 4 , the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.Instituto de Física La Plat

Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces S³/Zp. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy in the high-temperature limit of the different lens spaces points out the appearance of a temperature-independent contribution of topological origin to the entropy. The remaining terms are exponentially suppressed by the temperature. The topological contribution to the entropy appears as a subleading correction to the Stefan-Boltzmann term of the free energy, and can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.Instituto de Física La Plat

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, M3, with constant curvature 6/a2. For masses lower than 2π/β, this term can be identified with the free energy of the same theory on M3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, Shol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy Shol 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. SUVtop > SIRtop. 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.Facultad de Ciencias ExactasInstituto de Física La Plat