Higher-derivative terms in one-loop effective action for general trajectories of D-particles in Matrix theory

TL;DR

This paper computes the one-loop effective action for D-particles in Matrix theory, revealing that higher-derivative terms vanish only for straight-line trajectories, challenging assumptions about non-renormalization properties.

Contribution

It provides the first explicit calculation of six-derivative terms in the effective action for general D-particle trajectories in Matrix theory.

Findings

Six-derivative terms vanish for straight-line trajectories.

Higher-derivative terms do not vanish in general trajectories.

Challenges assumptions about non-renormalization of certain fermion terms.

Abstract

The one-loop effective action for general trajectories of D-particles in Matrix theory is calculated in the expansion with respect to the number of derivatives up to six, which gives the equation of motion consistently. The result shows that the terms with six derivatives vanish for straight-line trajectories, however, they do not vanish in general. This provides a concrete example that non-renormalization of twelve-fermion terms does not necessarily imply that of six-derivative terms.