Bogolyubov Institute for Theoretical Physics,

14-b Metrologichna Str.,

Kyiv 03143,

UKRAINE

E-mail: vgusynin@bitp.kiev.ua

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

**Abstract:**

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.