Non-commutative tachyon action and D-brane geometry

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 $A$.

12 pages, no figures

References in corpus (4)

• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Star Products from Open Strings in Curved Backgrounds
• Noncommutative Differential Calculus for D-brane in Non-Constant B Field Background
• Making Non-Associative Algebra Associative

Cited by in corpus (7)

• Cyclicity of non-associative products on D-branes
• Quantum symmetries in orbifolds and decomposition
• D3-branes in NS5-brane backgrounds
• Nonassociative Field Theory on Non-Geometric Spaces
• Open-String Actions and Noncommutativity Beyond the Large-B Limit
• Non-topological non-commutativity in string theory
• On the Open String Ending on D-brane