Bogolyubov Institute for Theoretical Physics,
14-b Metrologichna Str.,
Kyiv 03143,
E-mail: vgusynin@bitp.kiev.ua

Points-strings-branes, gauge fields - geometry and the local conservation laws

The local conservation laws for the Maxwell, Kalb-Ramond, brane gauge fields are derived. Axial-tensor currents which have symmetry of the dual Riemann tensor satisfy conservation laws and Bianchi identities. The existence of an additional  symmetry with different signs for the energy-momentum tensors of gauge fields is established. For topologically massive gauge theory in d = 3, BF theories in d = 4, the transformation symmetry between gauge potentials and dual fields strengths
leads to the equations of motion and  the existence of conserved axial vector currents.