Curvature terms in D-brane actions and their M-theory origin

Abstract

We derive the complete (curvature) 2 terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the o(α ′ 2 ) corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3brane with trivial normal bundle, considerations of SL(2, Z Z) invariance lead to a complete sum of D-instanton corrections for both the parity-conserving and the parity-violating parts of the effective action. These corrections are required for the cancellation of the modular anomalies of massless modes, and are consistent with the absence of chiral anomalies in the intersection domain of pairs of D-branes. We also show that the parity-conserving part of the non-perturbative R 2 action follows from a one-loop quantum calculation in the six-dimensional world-volume of the M5-brane compactified on a two-torus. 2/991

Derivative corrections to the D-brane Born-Infeld action: non-geodesic embeddings and the Seiberg-Witten map

“…We show that the part of these corrections involving only the transverse scalars can be written in terms of the second fundamental form as required on general grounds. The resulting expression is shown to agree with a previous result in the literature [6].…”

“…The embedding is described by the objects ∂ µ Y M , which span a local frame of the tangent bundle and the ξ i M which play a similar role for the normal bundle (see e.g. [6] for further details). World-volume indices are raised and lowered with the induced metric…”

Generalized supersymetric boundary state

“…The absence of the O(α ′ ∂ 2 ) correction to the D-brane action seems to be universal (see refs. [11,12,19]). …”

“…(2.4) and (2.26) as 11) and the quantity B F (x) appearing in eq. (3.10) is obtained by substituting F (x) into the place of the constant F in |B(F ) .…”

“…However, as mentioned above, these D-brane actions have been obtained in only the leading order estimation with respect to the derivatives acting on the fields on the D-branes. The derivative corrections may ruin the intriguing properties which the D-brane actions possess, and hence a systematic method for evaluating higher order corrections of the D-brane actions and the boundary states are needed [11,12,13].…”