Renormalization of boundary fermions and world-volume potentials on D-branes

Abstract

We consider a sigma model formulation of open string theory with boundary fermions carrying Chan-Paton charges at the string ends. This formalism is particularly suitable for studying world-volume potentials on D-branes. We perform explicit twoloop computations of the potential T-dual to the non-abelian Born-Infeld action. We also discuss the world-volume couplings of NS fluxes which are responsible for Myers' dielectric effect.

On non-abelian low energy effective action for D-branes

“…This field redefinition also affects the terms containing higher powers of Φ, but unless we fix coefficients in the terms of the order more than Φ 6 , c can be set to 0. Also we see in (4.9), that the structure Tr[Φ i , Φ j ] 3 corresponding in the T-dual picture to the term Tr F 3 is absent, which agrees with the 3-point superstring amplitude for a gauge field and the papers [6,13,14,16] Now let us get the action from the partition function of the bosonic string. In this case, we have for the partition function the following expression…”

“…Let us calculate the Φ 6 -term. The details of the calculation can be found in the Appendix at the end of the paper, see also the papers [13,14,15]. The answer includes two structures…”

Boundary σ model and corrections to D-brane actions

“…Their computation involves integration over d 2 z and no integration over θ. Bulk integration can be done as follows [10]:…”

“…In [10] this model was used to study world-volume potentials on a stack of coincident D-branes and world-volume couplings of NS fluxes which are responsible for Myers' dielectric effect [14]. In this section we want to study the effect of introduction of non-trivial embedding of a stack of coincident D-branes in a curved target space.…”

“…When there are several vertices on the boundary one may worry that there will be many regions of integration corresponding to relative positions of the angles on the boundary. However, as was shown in [10] using the symmetry properties of the ξ propagators on the boundary and the fact that they are double periodic functions of angles it is possible to significantly reduce the number of regions. The perturbation theory becomes path-ordered like in ordinary quantum mechanics.…”