Abstract. We show that the BRST/anti-BRST invariant 3 + 1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to the coexterior derivative of differential geometry. There exists a bosonic symmetry which keeps the ghost terms invariant and it turns out to be the analogue of the Laplacian operator. The Hodge duality operation is shown to correspond to a discrete symmetry in the theory. The generators of all these continuous symmetries are shown to obey the algebra of the de Rham cohomology operators of differential geometry. We derive the extended BRST algebra constituted by six conserved charges and discuss the Hodge decomposition theorem in the quantum Hilbert space of states. †

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U (1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in θ. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order θ is also derived.

No abstract

No abstract