BRST Formulation of 4-Monopoles

A supersymmetric gauge invariant action is constructed over any 4-dimensional Riemannian manifold describing Witten's theory of 4-monopoles. The topological supersymmetric algebra closes off-shell. The multiplets include the auxiliary fields and the Wess-Zumino fields in an unusual way, arising naturally from BRST gauge fixing. A new canonical approach over Riemann manifolds is followed, using a Morse function as an euclidean time and taking into account the BRST boundary conditions that come from the BFV formulation. This allows a construction of the effective action starting from gauge principles.Comment: 18 pages, Amste

BRST QUANTIZATION OF NON-ABELIAN BF TOPOLOGICAL THEORIES

The off-shell nilpotent BRST charge and the BRST invariant effective action for non-abelian BF topological theories over D-dimensional manifolds are explicitly constructed. These theories have the feature of being reducible with exactly D-3 stages of reducibility. The adequate extended phase space including the different levels of ghosts for ghosts is explicitly obtained. Using the structure of the resulting BRST charge we show that for topological BF theories the semi-classical approximation completely describes the quantum theory. The independence of the partition function on the metric also follows from our explicit construction in a straightforward way.Comment: 13 pages, amste

A New Action Principle for Witten's Topological Field Theory

In this letter a new gauge invariant, metric independent action is introduced from which Witten's Topological Quantum Field Theory may be obtained after gauge fixing using standard BRST techniques. In our model the BRST algebra of transformations, under which the effective action is invariant, close off-shell in distintion with what occurs in the one proposed by Labastida and Pernici. Our approach provides the geometrical principle for the quantum theory. We also compare our results with an alternative formulation presented by Baulieu and Singer.Comment: 8 pages, SB/F-94-22

On the Interacting Chiral Gauge Field Theory in D=6 and the Off-Shell Equivalence of Dual Born-Infeld-Like Actions

A canonical action describing the interaction of chiral gauge fields in D=6 Minkowski space-time is constructed. In a particular partial gauge fixing it reduces to the action found by Perry and Schwarz. The additional gauge symmetries are used to show the off-shell equivalence of the dimensional reduction to D=5 Minkowski space-time of the chiral gauge field canonical action and the Born-Infeld canonical action describing an interacting D=5 Abelian vector field. Its extension to improve the on-shell equivalence arguments of dual D-brane actions to off-shell ones is discussed.Comment: 18 page

Topological mass in seven dimensions and dualities in four dimensions

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.Comment: 7 page

Matter Fields in the Lagrangian Loop Representation: Scalar QED

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the beta-gamma phase diagram of this model.Comment: 10 pages, LaTe

Non Abelian TQFT and scattering of self dual field configuration

A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It is shown that the phase space of the theory can be exactly quantized in terms of the space of holomorphic structures over stable vector bundles of degree zero over Riemann surfaces. The Dirac monopoles are particular static solutions of the field equations. Its relation to topological gravity is discussed.Comment: 13 pages, Late

BF models, Duality and Bosonization on higher genus surfaces

The generating functional of two dimensional $BF$ field theories coupled to fermionic fields and conserved currents is computed in the general case when the base manifold is a genus g compact Riemann surface. The lagrangian density $L=dB{\wedge}A$ is written in terms of a globally defined 1-form $A$ and a multi-valued scalar field $B$. Consistency conditions on the periods of $dB$ have to be imposed. It is shown that there exist a non-trivial dependence of the generating functional on the topological restrictions imposed to $B$. In particular if the periods of the $B$ field are constrained to take values $4\pi n$, with $n$ any integer, then the partition function is independent of the chosen spin structure and may be written as a sum over all the spin structures associated to the fermions even when one started with a fixed spin structure. These results are then applied to the functional bosonization of fermionic fields on higher genus surfaces. A bosonized form of the partition function which takes care of the chosen spin structure is obtainedComment: 17 page