Testing the fermionic terms in the non-abelian D-brane effective action through order $\alpha'{}^3$

TL;DR

This paper tests the non-abelian D-brane effective action's fermionic terms up to order α'^3 by comparing spectrum calculations in magnetic backgrounds with string theory predictions, confirming their consistency.

Contribution

It extends previous tests to include fermionic terms in the effective action, demonstrating their agreement with string theory at order α'^3.

Findings

Perfect agreement between spectrum calculations and string predictions for fermionic terms.

Validation of the non-abelian D-brane effective action up to order α'^3.

Extension of previous bosonic-only tests to include fermionic contributions.

Abstract

Recently the construction of the non-abelian effective D-brane action was performed through order $\alpha'{}^3$ including the terms quadratic in the gauginos. This result can be tested by calculating the spectrum in the presence of constant magnetic background fields and comparing it to the string theoretic predictions. This test was already performed for the purely bosonic terms. In this note we extend the test to the fermionic terms. We obtain perfect agreement.