Observables in Topological Theories: A Superspace Formulation

Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST invariance is associated to super Yang-Mills invariance. We provide and discuss the general solution of this cohomology.Comment: Prepared for International Conference on Renormalization Group and Anomalies in Gravity and Cosmology (IRGA 2003), Ouro Preto, MG, Brazil, 17-23 Mar 200

Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.Comment: No. RR-7826 (2011

Superspace Gauge Fixing of Topological Yang-Mills Theories

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ``shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in orderto determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type.Comment: 26 pages, no figures, Late

Propagating Torsion in 3D-Gravity and Dynamical Mass Generation

In this paper, fermions are minimally coupled to 3D-gravity where a dynamical torsion is introduced. A Kalb-Ramond field is non-minimally coupled to these fermions in a gauge-invariant way. We show that a 1-loop mass generation mechanism takes place for both the 2-form gauge field and the torsion. As for the fermions, no mass is dynamically generated: at 1-loop, there is only a mass shift proportional to the Yukawa coupling whenever the fermions have a non-vanishing tree-level mass.Comment: 13 pages, latex file, no figures, some corrections adde

Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.Comment: 27 pages, Late

Incisivo lateral superior con dos raíces y dos conductos. Caso Clínico.

Las anomalías en la morfología del incisivo lateral superior son de muy baja frecuencia. Las anomalías de desarrollo radicular pueden presentarse como alteraciones tanto en el número de conductos, como en el número de raíces, así como en ambas regiones a la vez. En el presente trabajo, se reporta el caso de un paciente que se presenta a la consulta con malestar en el incisivo lateral superior izquierdo. En la radiografía preoperatoria se detectó la presencia de dos conductos y dos raíces, sin anomalía morfológica de su corona clínica, con requerimiento de tratamiento endodóntico. Concluimos que una correcta interpretación de las imágenes radiográficas preoperatorias es esencial, para poder detectar estas variantes y tomar las consideraciones necesarias para el adecuado tratamiento endodóntico.Fil: Martinez, P.. Universidad de Buenos Aires. Facultad de Odontología; Argentina;Fil: Boldo, M.. Universidad de Buenos Aires. Facultad de Odontología; Argentina;Fil: Corominola, P.. Universidad de Buenos Aires. Facultad de Odontología; Argentina;Fil: Sierra, L.. Universidad de Buenos Aires. Facultad de Odontología; Argentina;Fil: Lenarduzzi, A.. Universidad de Buenos Aires. Facultad de Odontología; Argentina;Fil: Fernández Solari, Jose Javier. Universidad de Buenos Aires. Facultad de Odontología. Cátedra de Fisiología; Argentina;Fil: Rodriguez, P.. Universidad de Buenos Aires. Facultad de Odontología; Argentina

Symmetry aspects of fermions coupled to torsion and electromagnetic fields

We study and explore the symmetry properties of fermions coupled to dynamical torsion and electromagnetic fields. The stability of the theory upon radiative corrections as well as the presence of anomalies are investigated.Comment: 9 pages, LaTe

Observables in Topological Yang-Mills Theories

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.Comment: 39 pages, Late

Vector Supersymmetry of 2D Yang-Mills Theory

The vector supersymmetry of the 2D topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behavior of the theory are analyzed.Comment: Some references adde