Perturbation Theory for Antisymmetric Tensor Fields in Four Dimensions

Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.Comment: 23 page

Time Measurement in Quantum Gravity

We discuss time measurement in quantum gravity. Using general relativity for large distances and the uncertainty principle we find a minimum time interval of the order of the Planck time, therefore the uncertainty in time measurment is bounded from below.Comment: 4 pages, TAUP-2087-9

Instabilities of noncommutative two dimensional BF model

The noncommutative extension of two dimensional BF model is considered. It is shown that the realization of the noncommutative map via the Groenewold-Moyal star product leads to instabilities of the action, hence to a non renormalizable theory.Comment: 9 page

Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of Algebraic Renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.Comment: Final version, typoes fixed. Revtex, 48 page

N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons

By constructing a nilpotent extended BRST operator \bs that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term \bs \Psi, if the gauge fermion $\Psi$ is allowed to depend on the inverse powers of supersymmetry ghosts. By using this nonanalytical structure of the gauge fermion (via inverse powers of supersymmetry ghosts), we give field redefinitions in terms of composite fields of supersymmetry ghosts and N=2 fields and we show that Witten's topological Yang Mills theory can be obtained from the ordinary Euclidean N=2 Super Yang Mills theory directly by using such field redefinitions. In other words, TYM theory is obtained as a change of variables (without twisting). As a consequence it is found that physical and topological interpretations of N=2 SYM are intertwined together due to the requirement of analyticity of global SUSY ghosts. Moreover, when after an instanton inspired truncation of the model is used, we show that the given field redefinitions yield the Baulieu-Singer formulation of Topological Yang Mills.Comment: Latex, 1+15 pages. Published versio

Topological BF Description of 2D Accelerated Chiral Edge Modes

In this paper, we consider the topological abelian BF theory with radial boundary on a generic 3D manifold, as we were motivated by the recently discovered accelerated edge modes on certain Hall systems. Our aim was to research if, where, and how the boundary keeps the memory of the details of the background metrics. We discovered that some features were topologically protected and did not depend on the bulk metric. The outcome was that these edge excitations were accelerated, as a direct consequence of the non-flat nature of the bulk spacetime. We found three possibilities for the motion of the edge quasiparticles: same directions, opposite directions, and a single-moving mode. However, requiring that the Hamiltonian of the 2D theory is bounded by below, the case of the edge modes moving in the same direction was ruled out. Systems involving parallel Hall currents (for instance, a fractional quantum Hall effect with \u3bd = 2/5) cannot be described by a BF theory with the boundary, independently from the geometry of the bulk spacetime, because of positive energy considerations. Thus, we were left with physical situations characterized by edge excitations moving with opposite velocities (for example, the fractional quantum Hall effect with \u3bd = 1 12 1/n, with the n positive integer, and the helical Luttinger liquids phenomena) or a single-moving mode (quantum anomalous Hall). A strong restriction was obtained by requiring time reversal symmetry, which uniquely identifies modes with equal and opposite velocities, and we know that this is the case of topological insulators. The novelty, with respect to the flat bulk background, is that the modes have local velocities, which correspond to topological insulators with accelerated edge modes

3D Dynamics of 4D Topological BF Theory With Boundary

We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The residual gauge invariance is described by means of two Ward identities which generate an algebra of conserved currents. We interpret this algebra as canonical commutation relations of fields, which we use to construct a three dimensional Lagrangian. As a remarkable by-product, the (unique) boundary condition which we found, can be read as a duality relation between 3D dynamical variables.Comment: 22 pages, no figures, version to appear on New Journal of Physic

Maxwell-Chern-Simons Theory With Boundary

The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The boundary is introduced according to Symanzik's basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge does not depend on the Maxwell term.Comment: 30 page

Nonrenormalization theorems for N=2 Super Yang-Mills

The BRST algebraic proofs of the the nonrenormalization theorems for the beta functions of N=2 and N=4 Super Yang-Mills theories are reviewed.Comment: 3 pages, contribution to SUSY 2000 Encyclopedi

BRST Cohomology of N=2 Super-Yang-Mills Theory in 4D

The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N=2 algebra. By the introduction of a set of suitable constant ghosts associated to the generators of N=2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N=2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge invariant polynomial $tr\phi^2$ and the complete N=2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N=2 beta function.Comment: 22 pages, LaTeX, final version to appear in Journ. Phys.