Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson Lines

Abstract

We write the recently conjectured action for transformation of the ordinary Born-Infeld action under the Seiberg-Witten map with one open Wilson contour in a manifestly non-commutative gauge invariant form. This action contains the non-constant closed string fields, higher order derivatives of the non-commutative gauge fields through the ${\ast }_N$-product, and a Wilson operator. We extend this non-commutative $D_9$-brane action to the action for $D_p$-brane by transforming it under T-duality. Using this non-commutative $D_p$-brane action we then evaluate the linear couplings of the graviton and dilaton to the brane for arbitrary non-commutative parameters. By taking the Seiberg-Witten limit we show that they reduce exactly to the known results of the energy-momentum tensor of the non-commutative super Yang-Mills theory. We take this as an evidence that the non-commutative action in the Seiberg-Witten limit includes properly all derivative correction terms.

24 pages, Latex, revised some parts in such a way that not to be concluded that the proposed non-commutative action is identical to the DBI action in the SW limit, references added

References in corpus (6)

• An Exact Solution to Seiberg-Witten Equation of Noncommutative Gauge Theory
• How Noncommutative Gauge Theories Couple to Gravity
• Deformed QED via Seiberg-Witten Map
• Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products
• Energy-momentum Tensors in Matrix Theory and in Noncommutative Gauge Theories
• Factorization and generalized *-products

Cited by in corpus (6)

• On-shell S-matrix and tachyonic effective actions
• Integer-Squared Laws for Global Vortices in the Born--Infeld Wave Equations
• S-matrix elements and off-shell tachyon action with non-abelian gauge symmetry
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity
• Gauge Invariance and Noncommutativity
• Multiple D${}_p$-branes as a D${}_{p+2}$-brane