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Central charge contribution to noncommutativity. (English) Zbl 1147.83314
Summary: In the presence of antisymmetric Kalb-Ramond field $$B_{\mu\nu}$$ $$Dp$$-brane, to which string endpoints are attached, is a noncommutative manifold. Adding linear dilaton field, $$\Phi(x)=\Phi_0+ a_\mu x^\mu$$, the coordinate in the direction of dilaton gradient, $$x_c= a_\mu x^\mu$$, becomes commutative, while the world-sheet conformal factor $$F$$ is a new noncommutative variable. In this article we demonstrate different approach to realization of quantum conformal invariance. We introduce Liouville action in such a way that world-sheet conformal factor $$F$$ does not spoil quantum conformal invariance and theory depends on arbitrary parameter, central charge $$c$$. Particular relations between background fields produce local gauge symmetries, which transform some of the Neumann into the Dirichlet boundary conditions decreasing the dimensionality of $$Dp$$-brane.
We introduce one methodological improvement regarding derivation of boundary conditions. Canonical Hamiltonian as a time translation generator must have well defined derivatives in coordinates and momenta. From this requirement we obtain boundary conditions directly in terms of canonical variables.
##### MSC:
 83E30 String and superstring theories in gravitational theory 83C65 Methods of noncommutative geometry in general relativity
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