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arXiv · hep-th/0203077

Non-commutative tachyon action and D-brane geometry

Manfred Herbst·Alexander Kling·Maximilian Kreuzer
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Abstract

We analyse open string correlators in non-constant background fields, including the metric $g$, the antisymmetric $B$-field, and the gauge field $A$. Working with a derivative expansion for the background fields, but exact in their constant parts, we obtain a tachyonic on-shell condition for the inserted functions and extract the kinetic term for the tachyon action. The 3-point correlator yields a non-commutative tachyon potential. We also find a remarkable feature of the differential structure on the D-brane: Although the boundary metric $G$ plays an essential role in the action, the natural connection on the D-brane is the same as in closed string theory, i.e. it is compatible with the bulk metric and has torsion $H=dB$. This means, in particular, that the parallel transport on the brane is independent of the gauge field $A$.

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Manfred Herbst, Alexander Kling, Maximilian Kreuzer. 2002-03-08. Non-commutative tachyon action and D-brane geometry. https://doi.org/10.1088/1126-6708%2F2002%2F08%2F010

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