Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta Function and Nonabelian Born-Infeld Action

TL;DR

This paper develops a framework for calculating curvature corrections to the nonabelian Born-Infeld action by deriving all-order derivative corrections in the abelian case, then translating these results to the nonabelian setting using the Seiberg-Witten map, and constructing a matrix model for ' corrections.

Contribution

It introduces a method to compute all-order derivative corrections to the abelian BI action and relates these to nonabelian corrections via the SW map, advancing the understanding of quantum dielectric branes.

Findings

Computed the 2-loop beta function for open strings in a WZW background.

Developed a new regularization method for 2-loop graphs.

Constructed a perturbative classification of nonabelian tensor structures.

Abstract

We initiate a programme to compute curvature corrections to the nonabelian BI action. This is based on the calculation of derivative corrections to the abelian BI action, describing a maximal brane, to all orders in F. An exact calculation in F allows us to apply the SW map, reducing the maximal abelian point of view to a minimal nonabelian point of view (replacing 1/F with [X,X] at large F), resulting in matrix model equations of motion. We first study derivative corrections to the abelian BI action and compute the 2-loop beta function for an open string in a WZW (parallelizable) background. This beta function is the first step in the process of computing string equations of motion, which can be later obtained by computing the Weyl anomaly coefficients or the partition function. The beta function is exact in F and computed to orders O(H,H^2,H^3) (H=dB and curvature is R ~ H^2) and O(DF,D^2F,D^3F). In order to carry out this calculation we develop a new regularization method for 2-loop graphs. We then relate perturbative results for abelian and nonabelian BI actions, by showing how abelian derivative corrections yield nonabelian commutator corrections, at large F. We begin the construction of a matrix model describing \a' corrections to Myers' dielectric effect. This construction is carried out by setting up a perturbative classification of the relevant nonabelian tensor structures, which can be considerably narrowed down by the constraint of translation invariance in the action and the possibility for generic field redefinitions. The final matrix action is not uniquely determined and depends upon two free parameters. These parameters could be computed via further calculations in the abelian theory.