**Conformal invariance in the presence of the world sheet conformal factor and (non)commutativity
of the Dp-brane coordinates**

**Abstract:**

The antisymmetric background field is a source of noncommutativity of the Dp-brane coordinates,
while the linear dilaton field turn the coordinate, in direction of gradient of dilaton field, to commutative one.
In the case where the conformal invariance is realized by inclusion of
the Liouville term, the theory is conformally invariant even in the
presence of the world sheet conformal factor F, and it depends on the new
parameter, the central charge c. As well as in the absence of the Liouville
action, for particular relations between background fields, the local gauge
symmetries appear in the theory. They turn some Neumann boundary conditions
into the Dirichlet ones, and decrease the number of the Dp-brane dimensions.

Joint work with *Branislav Sazdovic*.