Open-String Actions and Noncommutativity Beyond the Large-B Limit

TL;DR

This paper explores corrections to open-string effective actions beyond the large-B limit, revealing a deformed noncommutative product structure that extends the Seiberg-Witten framework.

Contribution

It introduces a boundary-state computation for corrections beyond the large-B limit and identifies a deformed non-associative product describing the amplitude.

Findings

Derived a metric-dependent deformation of the *2 product

Connected noncommutative deformations to boundary-state computations

Extended understanding of Wilson lines beyond the Seiberg-Witten limit

Abstract

In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the derivative expansion for open-superstring effective actions is naturally expressed in terms of the symmetric products *n. Here, we investigate corrections around the large-B limit, for Chern-Simons couplings on the brane and to quadratic order in gauge fields. We perform a boundary-state computation in the commutative theory, and compare it with the corresponding computation on the noncommutative side. These results are then used to examine the possible role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in fields, the entire tree-level amplitude is described by a metric-dependent deformation of the *2 product, which can be interpreted in terms of a deformed (non-associative) version of the Moyal * product.