Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace

TL;DR

This paper computes the beta-functions for an open string sigma-model with a U(1) background using N=2 boundary superspace, deriving the effective D-brane action and linking UV finiteness to stable holomorphic bundles.

Contribution

It introduces a three-loop calculation of beta-functions in N=2 boundary superspace, connecting UV finiteness to deformed stable holomorphic U(1) bundles.

Findings

Derived equations of motion with five derivatives on field strengths.

Obtained the bosonic sector of the effective D-brane action to four derivatives.

Linked UV finiteness to the condition of a deformed stable holomorphic U(1) bundle.

Abstract

We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the calculation. Performing the calculation through three loops yields the equations of motion up to five derivatives on the fieldstrengths, which upon integration gives the bosonic sector of the effective action for a single D-brane in trivial bulk background fields through four derivatives and to all orders in alpha'. Finally, the present calculation shows that demanding ultra-violet finiteness of the non-linear sigma-model can be reformulated as the requirement that the background is a deformed stable holomorphic U(1) bundle.